Why is this private key so long?
The extended private key (xpriv) is specified in
BIP 32.
It is not a private key to actively spend your funds, it is used to generate private-/public- keys for you to receive/send BTC.
The xpriv is 111 bytes long, compared to 32 bytes for a 'standard' private key.
The public key doesn't match with the unspent address in the account, so what is it exporting exactly?
Could you please elaborate what exactly you are referring to ?
If you have exported the xpub (extended public key), you can generate 'all future' public keys (and therefore also addresses) of your wallet.
If you want to have a backup, you need to export the xpriv key.