I got my Pixel 6 Pro in December (Japanese set) and had been suffering the widely reported Network issues (Mobile Data would come unavailable when moving around town; SIM Voice not allowed) and average battery life (due to Mobile Network being around 25-30%).
Having tried out different workarounds and hoping that an update would eventually fix the issues, I resigned myself to use Airplane mode several times during the day
However given that I cracked my screen, I went to Ctdi to fix it and raised also this issue. They were happy to replace my foreign set with a local refurbished unit and pointed that rather than a software issue it had to do with the motherboard.
So far on Day 1 this refurbished unit works great (17% mobile network usage), no connectivity issues.
Must say the technical service is very good, there is never any queues. So if anyone has issues, it's worth making a trip to Kallang.
Foreign models are replaced with a local refurbished unit (given they don't have spare parts); Local models they just proceed with replacing the motherboard.
Only drawback for both is that all your storage is wiped, even with cloud backup or cable data transfer it can be a pain to reconfigure everything (I have +240 apps installed

)