If the public address shown in your Bitcoin core wallet is the same as in your paper backup yes you should still receive the funds on the same wallet unless the address is changed after migration.
I hope next time before you upgrade your Bitcoin core to the most recent version always make a wallet.dat file backup just in case for future recovery.
I think to backup a wallet copying the wallet.dat file should be enough but if you want to backup the private key or the master private key you can use dumpwallet command sample command below
dumpwallet "yourwalletsname"
For a single private key, you can use this command below.
dumpprivkey "bc1sampleBTCaddress"
Without quotes.