Debian 12.1 upstream networking breaks in SSH sessions after running any Docker app

Docker Desktop for Linux
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N00b to Docker here - sorry to ask but I’m not actually sure what to search for or what to start with…

Debian 12.1 host - SSH is stock (OpenSSH_9.2p1). Installed Docker from standard instructions on the main site (so current release as of 29-08-23)…

I SSH into the system and do this – all is fine. Then after I run any Docker application (just running “ubuntu bash” for the test) – suddenly all subsequent SSH sessions lose upstream network access but I can still SSH into the host and existing sessions continue, just their own access to network resources breaks. This only happens for SSH sessions – if I’m at the machine’s console no issue, no loss of network access. If I run a Docker image from the machine’s console – this also didn’t seem to break network access for existing or future SSH sessions.

My intended use case is to run the server headless on a Debian 12.1 host on baremetal (I’m doing my testing in ESXi 6.5 guests) – I ran Ubuntu Server, Mint and Debian 11.7 to test this problem, only Debian 11.7 had the same behaviour and I’ve seen mentions that I think may be related but I’m not actually quite sure what to search for or where to actually begin.

I suspect the problem is with Debian which TBH really surprised me; given all this can anyone point me in the right direction? I don’t quite know what to look for.

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Can you explain this with more details?

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After running the docker application - I can no longer connect to any network resources (zero traffic out) from subsequent SSH sessions on the same host. Happens for all users, that said if I start an terminal session on the same host (no SSH) it works. It seems to tie in to the SSH daemon - it’s like the sessions conducted via that daemon lose access upstream. They can’t ping, lynx can’t browse, can’t traceroute, the works. They still work locally but anything off localhost is dead.