It all depends on how much you have in your ISAs and where you want to move them to. Your savings are each protected up to £85,000 per banking group – your wife and you each get that allowance, so it’s not split between married couples.
We’ve just published this article, which explains who owns which banks: https://www.moneymagpie.com/manage-your-money/who-owns-who-protecting-your-money-under-fscs-rules
As long as you spread any money over £85k (each) across different groups, you’re protected if your bank goes bust. It’s the same for the NS&I ISAs, too – anything over that amount isn’t protected, although the risk of that bank going bust is negligible because, as you say, it’s the only state-backed bank with Treasury support.
Hope that helps!