OEM Unlocking requires going online unfortunately, this is to check your IMEI/serial against a database to determine whether your device is subject to carrier restrictions such as those Verizon impose and have agreements with Google for.
However as you do not need to login to your/a Google account and as you do not wish to allow Google to connect your phone to your IP you would be best off visiting a coffee shop or local public library or such that offers free wifi to go through the OEM unlock toggle enabling process.
None of this is considered 'leaking' as it is intended and is required to use the service.
Once done and GrapheneOS flashed, the service no longer calls back when using the the OEM Unlock toggle as it isn't included in AOSP but just stock Pixel Experience. Not only that but ALL hardware identifiers other than Phone Model are hidden from any app or service including sandboxed play services. The ONLY time any other hardware ID would be further exposed to Google would be if you utilise the privileged eSIM management tool, the IMEI while being exposed shows no evidence this is harvested.
The only other 'consequences' to your privacy after flashing GOS would not come from the OS but would be any further voluntary disclosure of hardware ID's you choose to and voluntarily provide to an app, service or provider.