I am sorry, I don't really know but suggest it might be worth a test.

I remember that Umbrel uses Tor for making itself available outside of the local network in a way that felt a bit like magic.

I know Umbrel shipped their own official personal relay, which I found to work but be overall poor vs other options, although I only tested a very early version.

I know Umbrel also support Docker but I haven't tested it with a HAVEN Docker over tor.