Quote from: Bitcoiner2023

Does Bitcoin Core store the Account Extended Public Key or does it store the BIP32 Extended Public Key?

If you mean it like the terms used in iancoleman's BIP39 tool, then the imported (non-MultiSig) descriptors will contain the 'Account Extended Public Key'.
By definition, your "Account Extended Public key" is an "Extended public key" derived at the 'account_index'.
However, your "BIP32 Extended Public Key" can be easily computed from it since it is its non-hardened child.

If you want to check; use Bitcoin Core's wallet RPC: listdescriptors with the wallet "specter....../specter_wallet_name".

Quote from: Bitcoiner2023 on May 16, 2024, 10:09:14 PM

What does it actually look like when you set up a multi-sig wallet at Specter?
Won't the whole thing be more difficult to calculate, or does it make no difference whether single-sig or multi-sig?

Use the command above and you'll see that it also imported your Specter MultiSig Wallet's Extended Public keys to a watch-only Bitcoin Core wallet with the same name.
So there's no difference in terms of your concern about quantum computers computing your private key from your public key.

Quote from: Bitcoiner2023 on May 16, 2024, 10:09:14 PM

Since Bitcoin Core stores the pub key unencrypted on the computer, I wonder whether there would be a risk if I connected Specter to the Core.

You're supposed to connect your Specter wallet to a Bitcoin Core client that you own which will create a watch-only wallet that's locally stored, so I don't get the point.

Future-proofing your backup?