I had the same issue holding me back from giving up Windows, until I discovered the Python keyboard module.

How to bind key presses to it varies, but here's a recipe for Ubuntu, as an example:

https://askubuntu.com/questions/525482/how-can-i-assign-a-keyboard-shortcut-for-the-script-that-i-have-created#525495

Overall, it's not quite as elegant, as AutoHotKey, but it's ultimately a more powerful, since there's so much else I can also do from the same Python script.

Edit: Most notably, I don't recall AutoHotKey having any nice way to tell which apps are open, and Python can quickly call out to ps. It's been on my to-do list to leverage this to let me map keybindings according to what is open (i.e. a favorite game, or a move player.)