If you are leaving it at home, consider a WiFi-only tablet to eliminate any chance of data leaking through the cell modem. Or perhaps an Android emulator on a laptop, but that does come with its quirks. Better yet, also set up a router with router-level VPN at home just for your Facebook-connected devices. Get a cheap prepaid phone for the SMS activation. Don't boot anything up until you're ready and pay with cash or a prepaid gift card at a store you don't frequent or something like Craigslist if possible.

Normally, there's a chance of Google/Facebook asking for SMS confirmation again down the road, maybe long after your burner phone plan has expired. But you should be able to prevent this by adding a FIDO/U2F security key as your 2FA method. No idea if this can be set up on the mobile app, but if not, bring an unimportant laptop with a Linux live USB too.

Since you've already used Facebook in the past, and considering your use case and the nature of Facebook accounts, they most likely have your home location readily on file. Assuming that your main objective is to keep it from correlating your named accounts to pseudo/anonymous accounts and devices, first step would be to isolate it from your real IP address and browser fingerprint.

Now take everything to a library/cafe/somewhere you can access the internet anonymously. Leave your regular devices behind or at least have them in airplane mode and disconnected from the public WiFi. Set everything up, add your security key for 2FA, install a VPN client if Google/Facebook will allow it. Power everything down before leaving. Only power up the Facebook device once you are back home, ideally connected to a dedicated router with router-level VPN.

I don't really know how it all works, but sometimes I do think about all the times I've logged into accounts with my real name without a VPN. And wonder how many of those companies phone home to Meta with my real IP, letting them establish connections with my pseudonymous accounts I've also logged in to without a VPN.

It's a game rigged in their favor and the slightest mistake can blow your cover. Think carefully if Facebook is your only choice or if you can get by with an alternative. If you must use it, I would agree that a dedicated device, even if imperfect, is still one of the best measures for your privacy.

Is there some feature you need that is sprcific to mobile devices?

VPN + DeGoogled Privacy Android ROM would be the most practical. That way you should br free from most if not all cross device tracking.

In general having a seperate device for that stuff makes total sense.

Get some sort of device that is compatible with CalyxOS or GrapheneOS, like an older Pixel

not sure what would be best to handle verification.

You also have to be careful to use totally new accounts for everything on this new device, different number, different email, different device, different sim etc

There are apps like Tinfoil for Facebook.

You would have to get a burner phone to enable this.