But… PAKE is used as a method for ongoing exchange of messages

I don’t know what you mean.

In really don’t see it that complex, in my last job IT installed a passkey in my laptop

They can also install a randomly generated password just as easily.

Sending passwords is insecure because if an attacker gets the password, you lost

That is why you use a PAKE, you don’t send the password.

Old people won’t adopt it unless forced

They also won’t adopt passkeys unless forced. What is the difference?