I'm not sure. It depends if you exit through a spook exit node. I think that's a low probability, but I have a friend who thinks differently.
Discussion
I honestly don't think #tor exit node matters in this scenario.
If I use tor to connect to client online - the client does not know my IP but then the relays know the IP of the client.
So if this is client at my home - they know my home IP
Using #torborowser makes most sense to connect to untrusted sites - public clients. But then we are at my first question - how to safely login?
Have you tried using nos2x on TOR? I have not, but I use the bitwarden extention on TOR.