If your check determines that the backup is not healthy it should throw a Spatie\Backup\Exceptions\InvalidHealthCheck exception. The HealthCheck base class contains three helpful methods that helps you do this.
fail($message): will throw the right exception under the hood.
failIf(bool $condition, string $message): will throw the right exception if $condition is true
failUnless(bool $condition, string $message): will throw the right exception if $condition is false
You should register your custom health check in the health_checks key of the backup.php config file.
To see an example of a HealthCheck, go read the could of the MaximumAgeInDays and MaximumStorageInMegabytes health checks that are provided by the package.