Is Optimim your Internet provider?
Is the extender hard wired to the router?
Basically best bet is to run Ethernet cable from garage to a switch (Ethernet one not Nintendo

). This can be 1Gb or 2.5 Gb, depends on your internet connection. These are usually pretty cheap (you can just get unmanaged).
Plug in your PS5 into that (hard wired) and also your Google Mesh APs. Make sure to run Mesh in AP mode as otherwise you will have double NAT.
Alternatively if you have a few Ethernet ports on your Google setup, forget the Ethernet switch. Put the internet router in the garage in Bridge mode and use your Google Mesh system as the main firewall. Run PS5 directly to the main node. Not familiar with the Google setup so can't quite say what's best bet. But you can take your situation, drop it into ChatGPT/Gemini and get some ideas as well.