They absolutely do not record keystrokes and phone that home. You’re talking about the Intel Management Engine, which is completely useless to almost everyone, but there’s no evidence that it spies on you. There have been security vulnerabilities found in it that could let someone else compromise your system (notably: only if you’ve provisioned Intel Standard Manageability), but there is practically zero chance that Intel is doing that or even selling that sort of capability.

How confident do you need to be? I don't think I've seen any convincing evidence of any firmware spying in PC components.

Well, except the NSA's Clipper chip, but I don't think that really ever got implemented.

Well you can find a list of Libreboot compatible hardware here. I feel like your biggest issue, especially if you are relying on a prebuilt Windows PC, is all the bloatware they come with on top of Windows itself.

Lenovo uses proprietary, closed source firmware. There's no way to know what it's doing.