Can’t believe no one has mentioned this but how about launching ANY app from the dock? I can’t stand that I need to leave an app and switch context when I just want to add another app in split screen mode. Imagine a 9-dot icon on the left of the dock which brings up the spotlight search (probably in a new window on top of the running app or semi-transparent) and then you just drag-n-drop any app from there to split screen or slide over. This is #1 thing for me making “your next computer is not a computer” so untrue. Damn, is it THAT hard to implement?
I don’t think anything is hard to implement especially when it has been implemented somewhere else under the same libraries, UI/Web/Swift/etc Kits.
I find it insane that widgets are not the same on iOS and iPad, that makes no sense to me especially when they boast about the very first iOS being derived from OS X, iPadOS and iOS being the same base code, etc. Someone is lying, either iPadOS duplicates a lot of existing code from iOS and always has to play catch up, or the devices are not that quite compatible so there are other hardware requirements that we don’t know about (maybe inside the chips themselves and said libraries used), and spotlight and all that? Maybe not that much derive from OS X then... weather app? Calculator apps? If they can ‘Catalyst’ the heck out of apps back and forth, run iPhone apps in emulation mode on the iPad (remember those beginnings?), etc THEN WHY the feature parity is not 1:1 on the things that makes sense.
This does drive me mad a bit... I’ll chalk it to being a massive company with a lot of bureaucracy giving friction to absolutely every minor decision and action, far from agile for sure.
Hint: I think this could help for what you mean but needs a keyboard attached. On any app active, Cmd + Space for spotlight, pick from the suggestions or search for the app, on it do tap-hold then drag (what I find a confusing gesture specially in home) and place it on the right edge for split screen or around it for a floating app panel.