One option is, if you're having trouble exporting the private key(s), is to just send all of your btc to another wallet that uses a mnemonic phrase, and allows for keys to be exported. Problem solved.
It works in some cases but it's not what OP is asking.
In case OP needs that specific private key for verification purposes or just don't want to sync Bitcoin Core and import it elsewhere to spend, he can't do that.
This is why I also asked him on what he want to do with the private key so everyone can provide him a better option,
But sadly, he never replied.
It's such a simple solution if that's what you want, but if I recall correctly, the descriptor itself in some cases contains an extended private key - if not, then it's a watch-only wallet - and in such cases, you can simply use another software to calculate the derivation path in accordance to the descriptor wallet, which will then yield the private keys.