When I use baseURL as local host, all of my links still link to the served version on my website

That matters, it tells you you have no layout for home and page that way no pages are recreated but the content of your public folder stays as it is.

  • there’s something wrong with your local submodule import of the papermod theme.

  • check the status git submodule status

    a2eb47bb4b805116dcd34c1605d39835121f8dbe themes/PaperMod (v7.0-119-ga2eb47b)
    
  • update the submodule

    git submodule update
    

I’m not able to reproduce your problem using your repository. What I did

git clone https://github.com/onedeeper/mysite --recurse-submodules
Cloning into 'mysite'...
remote: Enumerating objects: 396, done.
remote: Counting objects: 100% (396/396), done.
remote: Compressing objects: 100% (126/126), done.
remote: Total 396 (delta 197), reused 381 (delta 182), pack-reused 0 (from 0)
Receiving objects: 100% (396/396), 824.96 KiB | 1.78 MiB/s, done.
Resolving deltas: 100% (197/197), done.
Submodule 'themes/PaperMod' (https://github.com/adityatelange/hugo-PaperMod.git) 
registered for path 'themes/PaperMod'
Cloning into 'C:/_repos/github/clone/mysite/themes/PaperMod'...
remote: Enumerating objects: 7462, done.
remote: Counting objects: 100% (40/40), done.
remote: Compressing objects: 100% (36/36), done.
remote: Total 7462 (delta 11), reused 21 (delta 4), pack-reused 7422 (from 1)
Receiving objects: 100% (7462/7462), 9.38 MiB | 1.70 MiB/s, done.
Resolving deltas: 100% (4410/4410), done.
Submodule path 'themes/PaperMod': checked out 'a2eb47bb4b805116dcd34c1605d39835121f8dbe'
hugo server
WARN  deprecated: site config key paginate was deprecated in Hugo v0.128.0 and will be 
removed in a future release. Use pagination.pagerSize instead.
Watching for changes in C:\_repos\github\clone\mysite {archetypes,assets,content,layouts,static,themes}
Watching for config changes in C:\_repos\github\clone\mysite\hugo.toml
Start building sites …
hugo v0.135.0-f30603c47f5205e30ef83c70419f57d7eb7175ab+extended windows/amd64 BuildDate=2024-09-27T13:17:08Z VendorInfo=gohugoio

WARN  deprecated: .Site.Author was deprecated in Hugo v0.124.0 and will be removed in a 
future release. Use taxonomies instead.
WARN  The author key in site configuration is deprecated. Use params.author.name instead.

                 | EN
-------------------+-----
Pages            | 21
Paginator pages  |  0
Non-page files   |  0
Static files     | 20
Processed images |  0
Aliases          |  7
Cleaned          |  0

Built in 43 ms
Environment: "development"
Serving pages from disk
Running in Fast Render Mode. For full rebuilds on change: hugo server --disableFastRender
Web Server is available at http://localhost:1313/ (bind address 127.0.0.1)
Press Ctrl+C to stop
here's the result of the generated home page:
<!DOCTYPE html>
<html lang="en" dir="auto">

<head>
	<meta name="generator" content="Hugo 0.135.0"><script src="/livereload.js?mindelay=10&amp;v=2&amp;port=1313&amp;path=livereload" data-no-instant defer></script><meta charset="utf-8">
<meta http-equiv="X-UA-Compatible" content="IE=edge">
<meta name="viewport" content="width=device-width, initial-scale=1, shrink-to-fit=no">
<meta name="robots" content="noindex, nofollow">
<title>udesh</title>

<meta name="description" content="">
<meta name="author" content="">
<link rel="canonical" href="http://localhost:1313/">
<link crossorigin="anonymous" href="/assets/css/stylesheet.01e04f4f86ae4dc2260171c32fa67a7e225672ca47849727998e24982bc3323a.css" integrity="sha256-AeBPT4auTcImAXHDL6Z6fiJWcspHhJcnmY4kmCvDMjo=" rel="preload stylesheet" as="style">
<link rel="icon" href="http://localhost:1313/favicon.ico">
<link rel="icon" type="image/png" sizes="16x16" href="http://localhost:1313/favicon-16x16.png">
<link rel="icon" type="image/png" sizes="32x32" href="http://localhost:1313/favicon-32x32.png">
<link rel="apple-touch-icon" href="http://localhost:1313/apple-touch-icon.png">
<link rel="mask-icon" href="http://localhost:1313/safari-pinned-tab.svg">
<meta name="theme-color" content="#2e2e33">
<meta name="msapplication-TileColor" content="#2e2e33">
<link rel="alternate" type="application/rss+xml" href="http://localhost:1313/index.xml">
<link rel="alternate" hreflang="en" href="http://localhost:1313/">
<noscript>
    <style>
        #theme-toggle,
        .top-link {
            display: none;
        }

    </style>
    <style>
        @media (prefers-color-scheme: dark) {
            :root {
                --theme: rgb(29, 30, 32);
                --entry: rgb(46, 46, 51);
                --primary: rgb(218, 218, 219);
                --secondary: rgb(155, 156, 157);
                --tertiary: rgb(65, 66, 68);
                --content: rgb(196, 196, 197);
                --code-block-bg: rgb(46, 46, 51);
                --code-bg: rgb(55, 56, 62);
                --border: rgb(51, 51, 51);
            }

            .list {
                background: var(--theme);
            }

            .list:not(.dark)::-webkit-scrollbar-track {
                background: 0 0;
            }

            .list:not(.dark)::-webkit-scrollbar-thumb {
                border-color: var(--theme);
            }
        }

    </style>
</noscript>
</head>

<body class="list" id="top">
<script>
    if (window.matchMedia('(prefers-color-scheme: dark)').matches) {
        document.body.classList.add('dark');
    }

</script>

<header class="header">
    <nav class="nav">
        <div class="logo">
            <a href="http://localhost:1313/" accesskey="h" title="udesh (Alt + H)">udesh</a>
            <div class="logo-switches">
            </div>
        </div>
        <ul id="menu">
            <li>
                <a href="http://localhost:1313/" title="home">
                    <span class="active">home</span>
                </a>
            </li>
            <li>
                <a href="http://localhost:1313/podcast/" title="podcast">
                    <span>podcast</span>
                </a>
            </li>
            <li>
                <a href="http://localhost:1313/personal/" title="writing/personal">
                    <span>writing/personal</span>
                </a>
            </li>
            <li>
                <a href="http://localhost:1313/academic/" title="writing/academic">
                    <span>writing/academic</span>
                </a>
            </li>
            <li>
                <a href="http://localhost:1313/misc/" title="misc.">
                    <span>misc.</span>
                </a>
            </li>
        </ul>
    </nav>
</header>
<main class="main"> 
<div class="post-content"><p>I&rsquo;m Udesh Habaraduwa.<br>
I believe humanity is good, valuable, and worth saving.<br>
I believe in the power of reason and science but worship neither.<br>
I believe problems are inevitable, solvable, and worth solving.<br>
I believe that, all else being equal, it&rsquo;s better to be free.</p>
<hr>
<p><strong>Note</strong>: This site is under construction. I am working on bringing my work, currently unorganized, into this space. Meanwhile, you can check out:</p>
<ul>
<li>My <a href="https://onedeeper.substack.com">podcast</a>.</li>
<li>My <a href="https://www.linkedin.com/in/onedeeper/">LinkedIn</a>.</li>
<li>My <a href="https://github.com/onedeeper">GitHub</a>.</li>
</ul>
<p>Thank you for your patience!</p>


</div>
    </main>
    
<footer class="footer">
        <span>&copy; 2024 <a href="http://localhost:1313/">udesh</a></span> · 

    <span>
        Powered by
        <a href="https://gohugo.io/" rel="noopener noreferrer" target="_blank">Hugo</a> &
        <a href="https://github.com/adityatelange/hugo-PaperMod/" rel="noopener" target="_blank">PaperMod</a>
    </span>
</footer>
<a href="#top" aria-label="go to top" title="Go to Top (Alt + G)" class="top-link" id="top-link" accesskey="g">
    <svg xmlns="http://www.w3.org/2000/svg" viewBox="0 0 12 6" fill="currentColor">
        <path d="M12 6H0l6-6z" />
    </svg>
</a>

<script>
    let menu = document.getElementById('menu')
    if (menu) {
        menu.scrollLeft = localStorage.getItem("menu-scroll-position");
        menu.onscroll = function () {
            localStorage.setItem("menu-scroll-position", menu.scrollLeft);
        }
    }

    document.querySelectorAll('a[href^="#"]').forEach(anchor => {
        anchor.addEventListener("click", function (e) {
            e.preventDefault();
            var id = this.getAttribute("href").substr(1);
            if (!window.matchMedia('(prefers-reduced-motion: reduce)').matches) {
                document.querySelector(`[id='${decodeURIComponent(id)}']`).scrollIntoView({
                    behavior: "smooth"
                });
            } else {
                document.querySelector(`[id='${decodeURIComponent(id)}']`).scrollIntoView();
            }
            if (id === "top") {
                history.replaceState(null, null, " ");
            } else {
                history.pushState(null, null, `#${id}`);
            }
        });
    });

</script>
<script>
    var mybutton = document.getElementById("top-link");
    window.onscroll = function () {
        if (document.body.scrollTop > 800 || document.documentElement.scrollTop > 800) {
            mybutton.style.visibility = "visible";
            mybutton.style.opacity = "1";
        } else {
            mybutton.style.visibility = "hidden";
            mybutton.style.opacity = "0";
        }
    };

</script>
</body>

</html>

You committed your public folder.

This contains old build files with the productive URL. As by before with the themes not working properly, there are no new pages generated/updated.

There’s (in most cases) no good reason to commit that. Better use a workflow, like this one from the docs Host on GitHub Pages | Hugo

If you really want to use and commit your locally generated public folder, you could use Static HTML By GitHub Actions

  • make sure you have a clean public folder before building (hugo won’t delete files there, just add/update)
  • test your site locally with hugo server
  • make sure you have no oild stuff in public
  • recreate the final version with just hugo and commit.