Non-root site path not working

Comments in the discussion referenced below mentioned a problem with URLs without trailing slash as opposed to with; to wit:

"So when I go my website on the subdomain without a trailing / the site doesn't work. So for example I have this deployed to https://www.algebraicjulia.org/blog/ but if you go to https://www.algebraicjulia.org/blog the website does not function correctly."

@cscheid responded "Can you open a new issue? We definitely want to fix this."

Commenter apparently never did. I'm doing it now because behavior is still the same.

Discussed in https://github.com/quarto-dev/quarto-cli/discussions/3615

^{Originally posted by michielvdmeulen December 9, 2022}
I'm trying to serve a blog on a non-root path, but despite following the instructions in the documentation I can't get it to work. My situation is identical to that in the docs, apart from different url naming of course, so something like this:

URL:
https://example.com/mysite/

_quarto.yml:

website:
  title: "My Site"
  site-path: "/mysite/"

When I render the site with and without the site-path option and compare the generated index.html file in the _site folder, both are exactly identical - even when I have completely deleted and re-rendered the content. In fact, only the _site\site_libs\quarto-nav\quarto-nav.js file has one line difference:

Apparently, this is either not enough or is not picked up on the server side. I'm using the latest Quarto version (1.2.269).

Does someone have an idea what could be wrong? Any help would be highly appreciated!