How can I recover my Bitcoin Core wallet after encrypting it with a password?

This depends on when this wallet was created. Quite old wallets used independent private key pools. IIRC, Bitcoin Core maintains a keypool of 1,000 unused keys and repopulates them with new random keys when the wallet receives a payment. In this wallet approach, backups of popular wallets will eventually become outdated once all keys in the original backup are funded and new payments are received to the address created after the backup was created. IIRC, that keypool default size may have been increased to 10,000 at some point, but the general problem persisted.

In 2016, Bitcoin Core 0.13.0 was released. Deterministic key generation based on BIP 32: Hierarchical Deterministic Wallet Added to Bitcoin Core wallet. If your wallet was created with a previous release, you may have deleted the only copy of your keys and have no recourse. If your wallet was created on Bitcoin Core 0.13.0 or lower, you can recover your funds by rescanning the blockchain.