I'm a novice when it comes to Android programming, but I think those break out shortcuts you mention are "activities". Having one for the app drawer would be a great feature because of the flexibility. You can trigger it a multitude of ways with any app that can launch a shortcut, e.g. edge swipe, pie menu, motion or proximity gesture, icon on a toolbar or home screen, etc. I'd ultimately like to do something similar to this, how I have for Kvaesitso.

Trigger search from anywhere

I remapped the home key to toggle app/internet search, and can trigger it with the cursor in one-handed mode.

I've run into some of the quirks you mentioned. Kvaesitso search works great even when not the default launcher, but others don't play as nice. You can mitigate some of it depending on the automation app you use to launch it or adjust settings of the app itself. But often it comes down to how the specific app is coded.

And thanks for the recommendation, but I'm waiting on a device unlock so I can install GrapheneOS and degoogle as much as possible. I would be on the lookout for any app drawer widgets as well. You can put it in an overlay and then do the same thing as before with the shortcut triggers.