I recommend using WebM container with VP9 codec instead of GIF if you are exporting it for web. It even supports alpha.

I have written a small blog post about how to Bypass CGNAT, and have also mentioned why you should not use Cloudflare if you are hosting for privacy.

Handbrake is great. But I would also recommend using Kdenlive. It is a video editor but if you just open your video in it and just export the project, you will get some good output format options.