TL;DR some instances will be restarted and a couple of minutes of downtime
OK! So, I believe I found what was driving me crazy for the past 48 hours and it should be the source of this: https://github.com/tootsuite/mastodon/issues/8263
I used OVH Debian image and didn't notice the /var partition size that it auto creates. I was randomly hitting out of space inside the containers because of /tmp files.
I am going to move Docker outside of /var and we should be good :)