Actually the relevant template should be placed under /layouts/section/shows.html/
Also I will give you one more hint @blablabla (before you say that you still do not see anything rendered with the template path I specified above).
The /shows/ section (as things are currently setup) does not contain regular .Pages, but instead Nested Sections due to your use of _index.md in every directory. Had you used index.md then these directories would have been regular .Pages.
So to populate the list under /shows/ (while keeping everything as is), you need to wrap everything right after the <main> tag within a range function and use the .Sections variable.
One last thing from me. The above template lookup PATH suggested by @brunoamaral is also correct.
However it all comes down to personal preference when it comes to maintaining a project.
Say you need custom layouts for several section lists.
With the above PATH you would need to create directories for each section under /layouts/<Section Name>/list.html
With the PATH I suggested you only need to create one directory under /layouts/section/<Section Name>.html
I always prefer to have as few directories as possible in a Hugo project (I h8 repetitive clicks).