@danielunited, @hrvoje_hr, @Kylo, @northeaster, @tolgaaaltas, I have been working on this extension, so far it looks like this:
This extension adds a button to the toolbar, when clicked opens this modal. When a GIF is selected from this Modal it inserts that GIF into the Post. There is still a few things to add, I have to still add a 'Loading...' feature, 'No results' feature, fix some minor bugs and try to make it as fast as I can. It will take some more time to complete this but as of now I have a working prototype.
You can sponsor this project here: Donate on PayPal.
Note: I have never taken donations on PayPal before, so if you encounter any errors please let me know.