My problem is solved. I don't know if you need to mark it up in the topic or something ? @calbzam
The problem was completely on Github and LFS side (and mostly on mine) since there are multiple LFS bandwidth to check with Github.
If you happen to have the same problem, make sure you check both personal LFS bandwidth and organization LFS bandwidth. It is a bit unclear when any of those are consumed since in the day to day usage, my personal one was reacting and when I wanted to gitsync, the organization one was...
Bandwidth for LFS : https://docs.github.com/en/github/setting-up-and-managing-billing-and-payments-on-github/viewing-your-git-large-file-storage-usage#viewing-storage-and-bandwidth-usage-for-an-organization
Thank you Carlos for the help,
Regards,
Thomas.