The setting that controls the property page URLs in your Google Vacation Rentals feed is Additional Property Slug Source.
In the HomeRunner plugin, go to Sync → Source Mapping and set Additional Property Slug Source to Source Id. Each property’s page URL then uses the listing ID from your PMS. This is the same ID the Google feed sends as the partner hotel ID, so the two always line up.
If you do not see a setting with this exact name, contact support to confirm its current location. Plugin settings occasionally get renamed or reorganized.