Authentication tokens… sessions still active. It is a thing…
First sentence… why state that if it does not matter. You sound like somebody that would setup an hour meeting to talk about everything not related to the meeting only to get to the crux of the matter in a single sentence.
That last sentence tells me you don’t use MFA. Use it then you don’t need to worry as much about a compromised password as long as you don’t use that same password somewhere else. My normal stance is… MFA everything, unless you really don’t care about it.
EVE Launcher even tells you… don’t do this as it is not secure, which is why MFA here is even more important. By clicking on that remember this account it creates an authentication token that says trusts the connection from this computer in a file on your pc. So your new password will be needed when you log into the services that isn’t via the browser or when you remove and add the account again to the launcher.