I haven't seen much discussion on how this specific attacker entrypoint can be mitigated. So I'm going to make a naive attempt in this comment.
How about storing the client's IP address in the session cookie. Then whenever the server recieves the cookie, it compares the client's IP address against the one stored in the session cookie. The server denies the login if there's a mismatch. The cookie would of-course have to be signed(hmac etc) so that it is tamper proof.
One problem with this is that client IP addresses are easily spoofed[2].
So, instead of storing the client's IP address; how about we instead store the clients' SSL fingerprints[3][4]. I haven't looked much into the literature, but I think those fingerprints are hard to spoof.
1. https://circleci.com/blog/jan-4-2023-incident-report/
2. https://adam-p.ca/blog/2022/03/x-forwarded-for/