I still haven’t been able to find any useful logs, so I’m not sure, but I suspect that the server is not able to see the bridge running on my local machine. 127.0.0.1 is likely getting routed into the container, not the host, so it doesn’t see the bridge. You could probably fix this by passing the port from the host to the container, but I don’t really want to mess with the bitwarden script, so unless I want to expose my bridge to the Internet, I don’t think I’m going to be able to use ProtonMail.
Which is just as well, I probably don’t really want to be doing that. This is just for my family, but I still don’t want to route automated emails through my personal account. I also think ProtonMail might not really like me doing that.
The solution I’m leaning towards now is Mailgun, which is actually suggested by the bitwarden documentation.
They have a free trial you can use without a credit card and it worked just fine with my bitwarden install. And the pricing is really tolerable, only $0.80 for 1000 emails per month. For my purposes that’s luxurious.
You can still send the automated messages from your custom domain. As long as you don’t edit your MX record, normal email receipt through ProtonMail shouldn’t be affected.
I have some other stuff that I will be self-hosting in the future, so this seems like the best long term bet.