recover private key – Can I restore an additional address of Bitcoin Core

Once in Bitcoin Core I created an address to receive some payments from a faucet. After years I reopened the Bitcoin Core and started to synchronize it. After a while there were a crash, and I decided to remove the previous Bitcoin Core folder (it appeared to be in a USB hard drive and didn’t get to Recycle Bin – when I decided to restore the removed files it was too late).
Then I reinstalled the Bitcoin Core, put there a wallet.dat from backup and successfully synchronized the blockchain. But I discovered – there’s no address for the faucet, which I needed and there’s no satoshi I expected. Apparently I created it before the backup (some previous history was there – so the wallet was restored – but without the latest address). So, should I consider the value on this address lost?

I tried to create the dump (dumpwallet "dump.txt") and to find the master private key there to restore the private key of this address somehow. The dump file contains some # extended private masterkey (starts with xprv). Also I know the address, which I set to the faucet (1J2ia2JZVoN8fqdvGYjkVaaX3A2C5BZzwj). So I thought I can use this data in “Mnemonic Code Converter” (https://iancoleman.io/bip39/) (extended private masterkey to BIP32 Root Key input and selected the Bicoin Core presets everywhere). Surprisingly enough the first generated entry contained my first default address, but I couldn’t find neither of the other addresses from the dump file. The address from the faucet doesn’t exist in the dump either. What do I do wrong?

Here is the wallet I’m talking about: https://www.blockchain.com/btc/address/1J2ia2JZVoN8fqdvGYjkVaaX3A2C5BZzwj