[Bug]: search does not work for websites with baseURL different than /

[xai]

What happened?

If a website using a baseURL like https://example.com/foo (i.e., using a subpath) enables the search fragment, a search triggers a GET request to https://example.com/index.json, which results in a 404 response and therefore in an empty search result regardless of the term queried by the user.

What did you expect to happen?

I would expect a GET request to https://example.com/foo/index.json, which would allow the search fragment to work as expected.

How can we reproduce this issue?

1. Set hugo baseURL in config.toml to something with a a subpath in the site url
2. Open website in browser of choice
3. Start network debugging feature in browser of choice
4. Trigger a search
5. Observe an empty search response on the site and a 404 response in the debugger

Is there anything else we need to know about?

I'll try to provide a respective PR asap.

Syna theme version

7fcac1f8

Hugo version

v0.78.1

Versions of other dependencies

No response

[stp-ip]

Great catch. Thanks for adding the fix as well.