I do not agree that it's being "prepared", it is being paranoid after a point. If you really want to, 10% of your portfolio could be USDT, and that way you could have some emergency fund.
But, I believe AT LEAST 10x of your emergency fund should be in BTCitcoin.
Of course, there's a level that you will build your emergency funds up to, you stop and take building up your bitcoin portfolio as your focus. If your emergency funds is already up to three months of your income, it's enough to take care of whatever unforeseen circumstances that can play out while you are investing and building your bitcoin portfolio.
Emergency might come or not, and it you use part of your emergency funds, you should refill it as soon as possible. Emergency funds should be in our local fiat currency for eash accessibility or you can leave it in USD, if the value of your local currency is a problem.