robinodds I'm sure there were other issues, but now I can't find them... Yay!
Anyways, a quick update. I've started looking into this, and have opened flarum/core2849. This includes some cleanup to the search state / search source system, but does not fix this particular issue. I've been trying to replicate the old behavior as I remembered it (searching while on a tag page shows results from that tag page, in that tag page). But I haven't been able to do that. The closest I've gotten while looking for old forums with the old behavior is that previously, going to a tag page while there's an input restricts the search to that tag.
That being said, I think the behavior I imagined makes sense (kinda like reddit: if you search while in a subreddit, it shows you results from that subreddit). However, it needs a fair bit of planning and discussion beforehand, so it will likely happen over the course of the 1.x releases.