The GPS satellites aren't receiving anything. The GPS satellites transmit signals, and the starlink terminals (and other users of GPS) receive those signals.
I don’t think the almanacs are necessary for the system to work, in theory. But I believe they’re commonly used by receivers to narrow down the range of possibilities when trying to find a PRN match for a signal they’re getting.
(I’ve dealt with GPS and similar navigation signals for work but am not an expert, this is just the impression I’ve gotten over a few years)