The problem is solved since 11:40 CET. We have been observing the situation closely after that.
A single OSD within our Ceph cluster at FRA3 was stuck in a "peering" state, which lead to some data read/write requests to hang (so, most things in VMs worked well, but some processes were blocking if they involved one of the affected placement groups).
While Ceph can perfectly work with placement groups that have only 2 of 3 OSDs available, "peering" (initiating connectings to the other involved OSDs to find consensus) is the only state where a placement group is not available for read/write requests, hence the processes on VMs being stuck despite 2 of 3 OSDs being available. After a restart of that single OSD process, peering worked fine and the VMs stabilized immediately.