Even without network logging, the hypervisor can still access the memory of the VM, parsing the kernel process and paging structures to read process memory, which can store transient logging information.
Things like AMD SEV/SEV-ES are designed to mitigate that aspect, the implementation of which can be proven to end-users of the VM by remote attestation.
That's not necessarily the case, vendors have VMs that can spin up with encrypted memory so that only the person spinning them up can see what is in the memory. All AMD and Intel processors have capabilities for this. Just in case you didn't know.
Sure you can. For example, with rsyslog you can just send all logs over the network to a logging server (which has disks).
That's the network, someone looking at the logs via ssh is also a leak by that logic. Of course!