Looks like search is not attempting to find a match against the URL of a Link post -- not even the domain name.

e.g., search on github.com

The search results will include Link posts with github.com in the title, Discussion posts with github.com in either the title or the description, or a comment or reply with github.com anywhere (including where the github.com is part of a URL). But search results will not include a Link post where the only Github.com is in that link post's URL.

You might already be aware of this exclusion, but if not I wanted to share it here. I can create an issue in the Github repo for it, if that is warranted.