You can import a your seed phrase into any other wallet, but you cannot add a passphrase or extension to the already existing seed phrase, not that it is possible but you will be creating another different wallet entirely and the funds on the existing wallet will need to be transferred to that wallet with pass phrase.
The term "seed phrase extension" is much more accurate. Using that term instead of "passphrase" would eliminate a lot of confusion.
I agree that the term pass phrase is kind of misleading but with the rate at which many wallets uses it, it’s better it is added in explaining to newbies to avoid further confusion when they got to see them on wallets.
Also I do somehow I think it is a passphrase to the seed phrase it is added upon, although technically it’s not because having alone is useless but you definitely need it to go through that wallet and if not you will be recovering a different wallet