Check if HangFire.JobStorage is instantiated

You could use the Hangfire.JobStorage.Current static property itself to check Hangfire storage configuration:

//InvalidOperationException " JobStorage.Current property value has not been initialized"
var storage = JobStorage.Current;

GlobalConfiguration.Configuration.UsePostgreSqlStorage(vaildConnString);

//no exception
storage = JobStorage.Current;

Moreover, you could query a database to test the connection:

JobStorage.Current.GetConnection().GetRecurringJobs();

Considering exceptions, I think that throwing an InvalidOperationException instead of something like SqlException is correct. Hangfire core isolated from details of a specific database.