Thanks a lot @gerhard. I actually just created a different bucket and changed the setting to point there (I mean, I now have one bucket for the uplinks an one bucket for the backups).
I run a manual backup twice, and it worked. I can see the files are in the bucket via the DigitalOcean interface, but the dedicated Discourse Backup page still times out with the same error when trying to do a listing of the bucket content.