Honestly the best screenshot software I've used so far is KDE's built-in printscreen thingy. I think it's called Spectacle. Does exactly all of the things you want - easy copying of regions, recording videos of regions (Wayland only unfortunately), annotation, etc.
One of the few times in Linux land where the UX is actually significantly better than Windows or Linux, and there's basically no jank at all.
(The only slight jank I noticed is that on X11 the "Screen recording" button just ... doesn't do anything. No "you need Wayland" message. Just nothing. I'll give it a pass though because the rest is so surprisingly great. Good job Spectacle authors!)
I do use ShareX on Windows for video recordings but Spectacle is better.
Spectacle is great. I tried to switch to it from Flameshot a few months back since it has all the features that I use regularly in Flameshot but ran into an issue where it would 2-3 times longer than Flameshot to start up when starting it up through the CLI. I use keymapper to map all my keyboard shortcuts and starting Spectacle using Qdbus is very slow compares to flameshot, like 1-2 seconds of waiting after pressing the hotkey compared to Flameshot being instant.
Looks like someone found a workaround by having spectacle run as a systemd process and restart after closing though, I'll have to give it a try: https://discuss.kde.org/t/make-spectacle-launch-faster/38030...