Will my apple watch still work if I switch to a service provider (Three) that doesn't suoport it

Hello, I’m new to apple watches, just got mine 4 months ago and I love it. It’s a cellular, SE3. I’ll have to switch service provider in the next week and I don’t fully understand what will happen if it doesn’t support apple watch. Ok, the cellular function won’t work, but will the rest be fine? Will it still be able to connect and sync to my phone, and use gps data on runs and exercises? Will it be just like when I turn data off?

Thank you for your help in advance!