Let's say, for example, that I accidentally entered my Microsoft account password instead of my Google account password when logging in to some Google web service. After getting an error message, I entered the correct password. Since the connection is HTTPS, only the Google authentication service¹ should have "seen" my Microsoft password.
How badly do I need to change my Microsoft account password after this incident?² Is there maybe some kind of certification that those companies undergo that can give me some confidence that failed password attempts won't be logged?
¹ ...and, obviously, the NSA, but if they want to access my Microsoft account, they can just directly ask Microsoft.
² I am aware that changing passwords regularly is good practice, so let's pretend I'm asking purely out of scientific curiosity.