Similarly, I use Firefox on Linux but I also regularly browse the web or post to HN on a phone that's been heavily deloused of Google using Firefox and other browsers—but never Chrome.
When I say register, I meant sign up for the wireless service. I did not already have an account. I was on my wifi and browsed to the wireless provider to activate my sim card and get a phone number. I could have done this on my PC but doing that on my cell verified with the vendor that my phone was supported since I am using an off-brand device. It was easier to copy the IMEI that way.
For Googles app store I used a throw away Gmail address that is not used anywhere else. I would love to put a new image on the phone but AFAIK there are no custom roms for my make/model of device. I would love to install GrapheneOS but they have sadly limited device support to Pixel. I am learning more about using adb since this is my first smart phone and with time I will neuter Google without replacing the rom, hopefully. It's mostly harmless for now since I rarely have the phone on.