In the case of "blocked: Vault health check failed", the vault service is still running and able to recover when MySQL gets back up. In the case of "blocked: Vault service not running", it won't recover on its own but systemd has detected the service as failed, so indeed it should be possible to solve the issue by tuning Restart*= on the systemd unit.
In the case of "blocked: Vault health check failed", the vault service is still running and able to recover when MySQL gets back up. In the case of "blocked: Vault service not running", it won't recover on its own but systemd has detected the service as failed, so indeed it should be possible to solve the issue by tuning Restart*= on the systemd unit.