If your transaction includes a UTXO assosiated with the 21st address, the gap limit is 20 and you haven't generated more addresses, your cold wallet can't sign the transaction?
Correct me if I am wrong please.
As I mentioned in the last part, I've tested that before posting.
I tried it with the UTXO associated with the 120th address (
index 119) of the watch-only wallet and the offline Electrum can still sign it.
If you parse the PSBT, you'll find details of how to find the correct private key.