Does "hook_ENTITY_TYPE_load" have performance advantages over "hook_entity_load"?
The only difference is that hook_entity_load() is invoked for every entity loaded, while hook_ENTITY_TPE_load() is invoked for every entity for which the entity type is ENTITY_TYPE.
If a module implemented hook_entity_load() only to handle a specific entity type, or a group of entity types, but not every entity type, its hook_entity_load() implementation would need to check which entity is being loaded, but since the second argument passed to the hook ($entity_type_id) is the entity type, checking that isn't time consuming nor a performance issue.

As for using hook_entity_load() or hook_entity_storage_load(), the second hook is invoked for content entities (not configuration entities) with a storage handler that saves the data in the database. In the other cases, including entities loaded from the entity cache, only hook_entity_load() is invoked.