I read OP's mention of third party cookies as an example of browsers supposedly moving in a more privacy focused direction, not as being related to authentication.
Well, the weird thing about the phrasing is the claim that third-party cookies are being phased out to "prevent this sort of thing"—where "this sort of thing" is "remember this device".
This is... sorta true? Insofar as creepy advertisers also "remember this device". But a first-party site storing a cookie to remember a login session is not at all in the same category for me.
