I was curious about this issue, so I loaded the website
https://hamlog.it/ to see what would happen. I thought all access might be blocked, but note that one can allow a security exception in the browser to load the login page. Remember here, your login will no longer be encrypted, but if you have lost your records it might be worth it to log in one more time to do a full export of the database.
PS: CloudSync v2 on the HamLog Android app still works.
PPS: HamLog is no longer on Google Play but 'HamLog NT' is there.