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grapheneosts as far as privacy goes Google only gets what you give it data wise and you can delete and opt out of having a persistent advertising ID.
You can go another level and never even login to Google by using Aurora Store but this restricts access to paid apps.
The rest of the experience benefits from ALL the privacy and security enhancements as listed on the features page:
https://grapheneos.org/features
Even if you did login to Google using it as close to the stock 'Pixel Experience' as you can, GrapheneOS is still head and shoulders above stock.
I would however postpone until the transition to Android 13 is complete and a stable release of it available for use with the web installer. Especially in relation to this:
https://discuss.grapheneos.org/d/486-warning-for-6th-gen-pixel-owners-looking-to-flash-grapheneos/15