It seems to me that this should be a simple Conditional Drop Down (CDD) setup. Nothing fancy and no Automations.
As you Add child record Tests to the Request the child record can know from a lookup field from Requests what the user has selected for the Test Category (or preferably bring down the [Related Test Category] and call it [Record ID# of Test category] ) down on the test record.
Then set up the CDD to filter the choices for the tests based on the [Record ID# of Test category] matching the [Related Test Category].
