I'd like to be able to search monsters for monster features like: Innate spellcasting, regeneration, [regular] spellcasting, multiattack, amphibious, keen hearing, sight, and/or smell, pack tactics, and flyby, to name a few off the top of my head.

I don't think this would be hard to implement, and it would be immensely helpful.

This should be easy to implement by adding a "Special Traits" filter field to the Advanced Filters section in the Monsters list, allowing filtering based on those listed traits.  This is already something listed in each monster block, standardized (at least for official content), and I imagine is already indexed.

Alternatively, some of this would be doable by expanding the tags on monsters, but that sounds like more work.  For example, there's no "innate spellcasting" tag, so someone would need to tag each such creature appropriately (tedious).

Or they could make a search box that lets us search for anything in monster stat block.

I just realized I needed this today when I wanted to look up something a trait I kind of remembered, but I didn't know what monster to look for it.

Something like our spell list or feature list, with an index of published monster abilities, and options to look at homebrew.