Usually with full-disk encryption, your supplied encryption passphrase is used to encrypt a single sector (or redundant set of sectors, spread across the disk) containing a much larger master key, which is in turn used to encrypt the rest of the sectors. When you change the disk password at the OS level, the master key remains the same (which is why you don't have to wait for the disk itself to re-encrypt); the single sector containing the key is just re-written to be encrypted with your new password.
Later, when you actually reformat the drive, you (or your OS) should spend some extra time writing over the sector(s) containing your encrypted FDE master key. But only those sector(s) need to be securely wiped. Even if someone can brute-force the password you used, they won't have that sector to use to turn it into a decryption key for the sectors; and they definitely won't be able to brute-force the FDE master key itself.
And, to make matters better, in systems with a TPM (most, these days), the TPM holds the FDE master key, and does the job of "shredding" it when it's no longer needed itself, as an async job kicked off by the OS along with the reformat. Also, in such systems, the FDE master key is never loaded into RAM, because the TPM itself does the sector-wise encryption/decryption as a DMA process.
You can overwrite a physical sector in modern drives, at least not in a standard way. That’s because they contain internal controllers that map physical to virtual sectors.
Later, when you actually reformat the drive, you (or your OS) should spend some extra time writing over the sector(s) containing your encrypted FDE master key. But only those sector(s) need to be securely wiped. Even if someone can brute-force the password you used, they won't have that sector to use to turn it into a decryption key for the sectors; and they definitely won't be able to brute-force the FDE master key itself.
And, to make matters better, in systems with a TPM (most, these days), the TPM holds the FDE master key, and does the job of "shredding" it when it's no longer needed itself, as an async job kicked off by the OS along with the reformat. Also, in such systems, the FDE master key is never loaded into RAM, because the TPM itself does the sector-wise encryption/decryption as a DMA process.