Compatibility question

I have an Eero 6 mesh router and 2 Eero 6 range extenders. One of them is in our 500 s.f. detached guest house which is 15 ft away from the main house which is 1670 s.f. Everything works fine but I am adding a Lutron Caseta Smart Bridge for the guesthouse which has a home theater and we want the flexibility of being able to dim the lights from our smartphones. The problem is the Lutron Bridge has to be connected to a router via an ethernet cable and there is no port on the back of the Eero 6 range extenders. They also do not make one that has an Ethernet port but I see there are other brands like Netgear that do make them. If I leave my two Eero 6 units in the house and just buy a Netgear range extender with the ethernet port will it work with the Eero or do I have to scrap the Eero 6 altogether and go with the same brand such as the Netgear? If so, which Netgear system would I need to buy and how many range extenders?