Did you try a browser you never use regularly, and log in using a private/incognito page?

Did you check your server's PHP config? Is Opcache on? My next steps would be to disable it (if running on Centos/Rhel). If nothing, then flush any other server caching features at server level, to see if it resolves your issue a conflict bottleneck.

If that fails, then you need to log into your underlying server command line for your WP instance (you can do the same on the server level for maximum discovery of info). Trying to log in via web browser.

When you are dropped out, run this journalctl command to see what traffic made it to the server sudo cat /var/log/messages | tail -n 100 followed by journalctl -b | tail -n 100. Then check security related server logs with centos sudo cat /var/log/secure or ubuntu with sudo cat /var/log/auth to see if the autologout was registered at server level. This should give you some clues as to the cause of the issue.

Be mindful--if you have server caching features (below wp level) on, check your cache TTL and store meta, before you disable managed server caching features. They can cause performance issues and break the site functionality if you don't do a server restart. In commandline sudo reboot to restart, or use a managed reboot function via your server providor's console (e.g. plesk) that runs that command.

Your url logging you out automatically may have other causes to php caching, as it sounds like a configured 302 redirect. Do you have a firewall active in front of your site like sucuri or cloudflare? They use AI and often treat your ip like a threat if it is in a CIDR with a blacklisted gateway ip.

Do you have a firewall active on your underlying server? firewall-cmd --list-all for centos/rhrel sever o/s commandline and sudo ufw status for ubuntu server commandline.

If still noting, then check your networking side starting with server configuration.

Check listening TCP/UDP connections: ss -tulp

Check network interface connections for UP DOWN: ip route show

Check your tcp packet journey from your local command line to your sever. Use host yourdomain.com (unified ubuntu/centos versio of nslookup which gives pub IP and NS) to get your server's public ip.

Use that public IP to trace your connection path from your local machine to your server looking for where it is dropped, using traceroute pub-ip and take it from there if a network issue.

If it fails, then ping the port from local commandline to see if its open nc -zv pub-ip 443

If still nothing, then provide more information.