schweizer Is there a risk that a Pixel 6 running GOS runs out of service if there are no 3g antennas?
Only if you have manually disabled 4G (LTE).
schweizer How do they know that I run a Pixel 6 at all?
Probably lots of ways they could know this (IMEI, various cellular radio characteristics or identifiers). This isn't something the OS can reasonably expect to hide.
schweizer Can I prevent unneccessary data transmission to my carrier? Such as version numbers and model names?
Only by not connecting to the carrier's network. Use WiFi only.