1. Foul. Some proponents of UCLA has been saying it was just a shoulder to shoulder challenge and therefore can't count as pushing. But if you look at the player send to guard the goalkeeper, the arm is clearly pushing back on the goalkeeper's chest.
2. Even if it's not a foul, it's still impeding. The striking player (at least at first) isn't making an attempt to play the ball, but to hold back the goalkeeper. The goalkeeper tries to move forward and rather than attempt to play the ball the striking player pushes her back into the net.
3. However, the most persuasive argument I've heard against is that the foul (whether a push or impeding) did not affect play? Why? Because to get a ball like this the goalkeeper needs to side shuffle towards the far post and then attack forward. Had the goalkeeper gone straight forward, the referee may have been of the opinion it would have gone over her outstretched hand since she made no effort to reposition herself laterally.
4. There's no rule prohibiting someone standing in front of the goalkeeper. It only becomes a foul once contact is made or movement is impeded instead of making a legit attempt to play the ball. GK coaches have recommended this be handled in two ways. One, the GK notify the ref before the corner is taken, try to move the striker (since they are both entitled to their space) or if not then engage in a shoving match with the striker prior to the corner being taken....particularly on a corner of this import. Physically move the striker or die trying. Two, a pusher. Particularly if the GK were already playing on a yellow, I would have gone with the pusher given the importance of the corner, but some GKs are too proud, some GK coaches think it's not the right way to handle things, and some coaches think it should just be on the GK. However, given the size mismatch, I think a pusher was warranted in this situation.
5. Part of this is on the GK. She unfortunately isn't very big relative to the other players. On the men's side, the goalkeeper just plows through the strikers who will lose any such shoving match. Therefore, it was imperative on her to try to sell the foul by falling over particularly once she had been pushed into the net and out of range of being able to impact it.
6. Isn't there limited VAR of these matches? If so my guess is the ref is hanging the hat on 3 and/or didn't have the angle on VAR to judge 3.