Column count of mysql.user is wrong. Expected 43, found 42. Created with MySQL 50518, now running 50641. Please use mysql_upgrade to fix this error.

In my case, and following the recommendation of the error message, I ran:

root@mysql-190877524-gm3j4:/# mysql_upgrade -uroot -p***
Checking if update is needed.
Checking server version.
Running queries to upgrade MySQL server.
Checking system database.
mysql.columns_priv                                 OK
mysql.db                                           OK
mysql.engine_cost                                  OK
mysql.event                                        OK
mysql.func                                         OK
mysql.general_log                                  OK
mysql.user                                         OK
Upgrading the sys schema.
Checking databases.
[...]
Upgrade process completed successfully.
Checking if update is needed.
That solved everything.