I have been happy with my Honeywell WiFi thermostat (T6 I think). I have it set up via the HomeKit integration, and block it from the Internet. Was relatively inexpensive and works well.

I prefer not to sync my information with Google or other entities either, but do not think that using Linux precludes using whatever tools they like. I don’t think this is a question about ideals, but about tools and compatibility.

I personally also doubt that Google Tasks supports that capability, unfortunately. I personally use Thuderbird for email on Linux, and it supports tasks too (I use Nextcloud for my tasks but I bet it supports Google as well). Not the same as your gnome extension, but an option.

Good luck!