The bus still operates from the Eagle terminal to T3 airside. It's currently designed for those passengers travelling on an American codeshare operated by Alaska.

The flight attendant often announces it on American flights arriving at T4 when there are passengers connecting to an Alaska-operated codeshare on board. The instructions provided are to take the bus from T4 to Eagle, then change bus to T3.

Although this has always been the case when changing from T4 to T3 and vice versa, it never strikes me as a "seamless" connection.