Matter devices on different Wifi

I have a new Nest thermostat in the garage that has a different wifi than in my home.
It is a Matter device that is only visible in the Google Home App and not in the Nest App. Because it can not be added to the Nest App, it does also not show in HA.
Is there a way to get this thermostat into HA ?
Options that I think of:
Can I add it as Matter to HA by temporarely moving it close to my HA and them move back to the garage and change wifi network ?
If I add the Google Home or Google Assistant Integration, will the thermostat then show in HA ?
Is there another way ?
Thanks

Although I have not used a Nest Matter thermostat, in theory …using the iOS HA Companion App on you mobile device, when in the garage, have the mobile device join the same WiFi network you want you Nest Thermostat to use. Then use the HA Companion App to add a new Matter device. The iOS mobile App will give the Nest thermostat the garage’s WiFi credentials which should allow the thermostat to join the garage’s WiFi network. This assumes your garage WiFi has a way to get to the HA Server without going through a router.

I will try this. Thanks.