Erroneously thinking that Percona develops Patroni. :D
IIRC, they may have made one or two contributions, but very minor.
But anyway, Patroni is orthogonal to pg_checksums.
As Michael already said, the following workflow works just fine (I did it dozens of times):
1. enable checksums on the standby node
2. start the standby and let it catch up with the primary
3. switchover to a standby node
4. enable checksums on the former primary (now replica).
Regards,
--
Alexander Kukushkin