With this info, I can conclude that the exported WIF private key isn't used as HD seed.
So for reference, using the "descriptor method" above should work in case Bitcoin Core is preferred instead of Coinb.in.

If the cosigners wishes to create their own cosigner wallets, they can replace the other party's private key with its public key instead.
And the other party doesn't even have to sync Bitcoin Core to co-sign the partially signed bitcoin transaction.