
Changing your password takes the current one plus the new one twice, and the current one is asked for so that a browser someone left signed in cannot be used to lock its owner out.
Where you have two-factor authentication switched on, the form asks for a current six-digit code as well, which closes the same door from the other side. A session on its own is not enough to change the password.
Passwords are stored hashed with Argon2id, and nobody with a copy of the database reads them back out. The board itself has no way of telling you what your old password was either.
The page itself: Account → Security → Password