I have started to think what is better for privacy
a) buy and old phone, on which someone most probably had been logged into google account, what assign phone imei to him/her and reinstall OS on the phone, e.g. to /e/
b) buy a new phone, with no Google login on it and use it with turning off as much Google as possible and using F-droid, probably with Aurora
Do the first. Once reflashed, the IMEI won’t be available to Google. Data such as IMEI is still available to Google Play services and apps, so any phone with that on it is still trackable by Google. They might not be able to tie an identity to it but, depending on what apps you install or use, it’s likely still possible. On a phone without Google services they can only get what you give them explicitly. So use a degoogled phone (e.g. e/OS/, Calyx, Lineage OS, etc) and, if the possibility exists on the phone, do not create or log in to any Google account. I’d also suggest avoiding any Meta properties too.
Either option is fine. I would base my decision more on my IT skills. If I had adequate IT skills I’d flash it myself, but if I were someone who didn’t know much about computer and just wanted some extra privacy, then I’d buy a pre-flashed phone.