feat: add json_output

[Janik-Haag]

This is useful if you have some other tool which makes use of the documentation data, e.g. a function search.

[infinisil]

Needs at least a test, but other than that and my comments, this looks good to me :)

[hsjobeki]

Regarding the whole Format, docbook, etc discussion. I think nixdoc should have a json Output as Default.
To loosen the coupling between nixdoc and the nixpkgs manual

[Janik-Haag]

Needs at least a test,

I added a test, and took the opertunity to refactor a bunch of tests, e.g. making the test_main function actually test the main function instead of just some copied code.

Regarding the whole Format, docbook, etc discussion. I think nixdoc should have a json Output as Default.

I think that this should not happen here, but (if at all) in a new major relase since it breaks current behavior.
Do you see this as a blocker for this pr?

[infinisil]

I don't think the default matters at all really, because I don't expect anybody to use this tool directly, it's all through automation. So definitely not blocking imo, this PR looks good as-is to me, thanks!