I'm working on a browser based, client side, GIF screen capture tool. Give it a try: https://gifcap.dev/
I needed to do this lately and my process was like: Make a window/screen capture with quicktime. Convert the capture to an animated gif with the ffmpeg command line utility. Find an easy image host to save the generate gif somewhere. This was all very cumbersome.
Your process even allows me to screengrab a single browser tab. Thank you so much!!!
It appears that everything is done clientside, but looking through the github code it's hard to imagine that it's done with so little code and no cloud/server side processing!