You can certainly do this, but not without customization of the theme, or finding a theme that is designed to do this (though I don’t know if any exist), unless you are willing to go with Option C below. Hugo’s tags work site-wide, and most if not all existing themes stick with that.
The approach you take depends on whether you want these tags to work only per section or work both ways, site-wide and per section.
Option A: per section tags
You probably should just use separate taxonomies as @maiki suggests, but then you’d have to override the theme to list on each page the section specific taxonomy rather than the global “tags” taxonomy.
Option B: global and per section tags
- the global tags indexes would be generated at
/tags as they normally would
- as @kaushalmodi suggests, you have to figure out how to, under
/projects/tags, generate the same kinds of pages generated under
/tags, but filtered by section. Not trivial.
- change the page templates so that the tags for the page link to the section specific index.
Option C: per section tags (alternate approach)
Treat each section with its own tag space as a separate Hugo site, which you would publish to a subdirectory in your webroot so that the end result would be a single site. You might have to make the right settings in Hugo for that to work (base URL? relative paths?).
I think A or C is easiest, depending.