The message is quite clear. There are to many open, valid API sessions. You remove "old" unused sessions from the web interface via Settings- >Web/API.
Sessions which have not expired (default timeout 300sec) are saved on Pi-hole shutdown and restored on restart. That's why you can fix the issue by restarting.
Default API session limit is 16.
I suggest you (temporarily) increase the limit, login and remove unused sessiosn
pihole-FTL --config webserver.api.max_sessions 17
This sounds reasonable. The software should be configured to open one API session, re-use it for it's activity and close it when it's done. Maybe something to report to the maintainers.