I think I solved it:
The A record in cloudflare had the cloudflare proxy enabled, but all CNAME records had it disabled.
Enabling cloudflare proxy on one of the subdomains made it work, but for Jellyfin this apparently isn’t allowed.
Disabling the proxy on the A record and all CNAME records, made it work.
I had the proxy activated for the A record since I set it up a few months go, so I don’t know why it stopped working just now…