Short comment here from experience… my parents are both now blues who haven’t flown for 6-7 years (well, other than private it you count that).

They have a household account, of which I’m not a part since I don’t share a household with them, but their Avios have been kept active by making occasional redemptions of which I’ve been the beneficiary. I might be having another come up shortly, by the way, just to help them out.

Since the Avios get taken pro-rata from both of their accounts, one redemption is enough to keep both accounts active for another 36 months.

BA also (usually…) sends emails saying Dear Mr./Mrs. OlderThanSchultzois, don’t let your Avios expire. So although it’s not so easy to look up the expiry date, it usually shouldn’t happen that they expire completely without warning. But it may require some surveillance on your part… FWIW, oneworld partner Alaska has a policy in which mileage plan miles earned don’t expire, but the account can be suspended or deactivated after two years (I forget the language) and restoring it is a matter of a phone call. Interestingly, there is no way there to see activity that’s even something like a year in the past, so it can be harder than with BA to know about it… but in contrast to BA, even if you forget about it for years, you wouldn’t actually lose all of them.

Editing to add: I’m reasonably sure the February 2024 date mentioned by the OP would correspond to membership renewal only, and is linked either to when you opened your Executive Club account, or when you had a Tier upgrade if you had one back when they reset your tier points whenever you upgraded tiers… but that’s awhile back.