Linux

I've used KShare for a while. Not sure if it's still under active development, but it's the closest thing I've found to ShareX, and works well enough for me

https://github.com/Gurkengewuerz/KShare

There's a few, but I really like Gnome Screen Recorder if you're using a gnome-based distro. I've also used Peek before which I believe has shortcuts as you said. To install Peek if you don't have the repository on your distro.

sudo add-apt-repository ppa:peek-developers/stable
sudo apt update
sudo apt install peek