Add a proper ci check for broken links and other issues in docs

[Kipok]

after looking more I don't think we changed ci, we just added strict: true parameter, right? If so, then mkdocs serve still worked fine with it, didn't fail with error. But ideally what we should do is we should add a new ci step that will just build the docs, not deploy them, so that we can run it in ci and hopefully configure to fail on any warnings, so that people can fix them before merging

Originally posted by @Kipok in #1204 (comment)