I don't understand satellite technology at all and how weather patterns affect signals, other than seeing that DirecTV sometimes says "no signal" when it's raining. Is Starlink going to have essentially the same issue?
Not exactly. Rain loss (actually called rain fade) can be countered with bitrate decrease. In case of DirectTV they would have to broadcast high and low bitrate streams cutting the number of channels by half if they already use all their allocated spectrum. DirectTV doesn't broadcast low bitrate streams for whatever reason so the signal is lost.
In case of LEO constellations with hundreds of satellites it should be similar to mobile networks that use adaptive modulation (that's standard since 2G). Receivers that get clean signal get high bitrate, Receivers that get poor signal get low bitrate. How good will Starlink be able to handle rain remains to be seen. Bitrate decrease will most likely be pretty significant, like 10 times.
