Keep in mind that if you "add" passphrase you actually create a completely new wallet, with new addresses. It's like you'd have one more wallet, with seed of 25+ words.
Why?
* Some can use that for extra safety by saving the seed in one place and the passphrase somewhere else.
* I've read that you can use this for plausible deniability. Keep a smaller amount in your normal wallet, keep the rest in the "special" one (but imho it's risky, you can too easy misplace your passphrase)
Exactly, the extension word (popularly known as passphrase) greatly increases the security and strength of the wallet, but we must be doubly careful, especially where to store this passphrase, but it isn't recommended to store it in the same place as the seed phrase, otherwise it's better to keep it without it.
So you have three secrets to safeguard: seed phrase, passphrase (the most important ones) and the encryption password to access the wallet locally through the file (default_wallet).
It should be used if the user is aware of the risks and responsibilities inherent to this.
I happened to came across few people who extended their seed phrases and now they do not care much about the seed phrases but only safe guard their passphrase, which is a wrong approach. They keep the seed phrases (that are hard to remember) on their emails or google drive and easy to remember passphrases in their mind. So they think it is a perfect security for their wallets as even if someone get access to their seed phrases, they would never find the passphrase.
This is NOT a correct way indeed. Extending the seed phrases may increase security but not in a manner as this one.