Looking for mesh setup to connect home and detatched garage

Leaving aside the math (40+42 does not add up to 110), it would help to know the composition of the external and internal walls of these buildings.

First: have you tried relocating the X6S extender to near the back door rather than in the garage?  110ft is just too far.

The general concensus is that Orbi devices can be moved apart until they no longer have a "strong" connection between them.  In a typical house, this is somewhere between 30 and 40 ft. but depends to a large extent on how many (and what kind of) walls are in the path.  So, it is entirely possible that a satellite 40-odd ft. from the router will make a good connection.  There is also a good chance that an outdoor satellite placed on the garage will make a good connection to the satellite by the back door, and also be able to provide service inside the garage as long as the garage walls are not something unfriendly to WiFi, such as several layers of brick or metal.

Mounting the RBS50Y outdoors poses all sorts of practical issues regarding the electrical supply.  And, the RBS50Y is frightfully expensive ($350 at Best Buy.  Not even sold by Amazon - only 3rd parties.)

My initial recommendation was going to be to purchase an Orbi RBK53 package (one router, two satellites) and attempt to locate the 2nd satellite inside the garage. You would know within minutes if it would get a good signal.  I bought that package from Amazon in August 2019 for $380.  (Just a few dollars more than the outdoor satellite and no electrial issues.)  Alas, when I search now, nobody seems to be selling the RBK53.  Either the pandemic has disrupted the supply chain, or Netgear has stopped producing them in favor of the new "AX" products.

Another possibility is to locate another WiFi extender by the back door.

Sorry not to be much help.