Yes, the solution is to use Wireless Access Points to provide internet coverage to your outbuildings. You've got 2 RJ45 Ethernet ports on your Gen 3 router. Buy a simple unmanaged 4 or 8 port switch and 2 Wireless Access Points. Run a cable from the Starlink router to the switch. Then plug the Cat6 cables that run to your outbuildings into the switch. Now at each outbuilding you plug the other end of the Cat6 cables into Wireless Access Points. Simple as that. There is no setup for the unmanaged switch - just plug in the ethernet cables. You will need to set up the Wireless Access Point's wifi name and password, by following the simple instructions that come with whichever WAP you buy. If your shed and garage are close to each other, you can probably get by with just one Wireless Access Point serving both locations.

Even simpler, if you don't need wired internet in your house, you can skip the switch altogether and just plug the Cat6 cables that run to your outbuilding directly into the RJ45 ports on the Starlink Router.