Your question is a bit unclear..

Later in the at-bat, the batter gets a solid hit. Is this scored as the batter reaching on an error, or getting a hit?

Well, when the batter gets a solid hit, does anybody playing the field make an error, or was it a clean hit?

The pop-up to the catcher has nothing to do with the solid hit. If the catcher drops the ball, that is an error on the catcher for that 1 play, but that play doesn't have any influence on the judgement of a future play.

Reaching on an Error means that the batter reached base safely on the current play due to a fielder making an error during that play, not from a past play.

The runs that are generated from the solid hit are earned. Again, the foul ball that the catcher made an error on has nothing to do with any other plays that come after that error.

Your question is a bit unclear..

Later in the at-bat, the batter gets a solid hit. Is this scored as the batter reaching on an error, or getting a hit?

Well, when the batter gets a solid hit, does anybody playing the field make an error, or was it a clean hit?

The pop-up to the catcher has nothing to do with the solid hit. If the catcher drops the ball, that is an error on the catcher for that 1 play, but that play doesn't have any influence on the judgement of a future play as far as how the batter gets on base

Reaching on an Error means that the batter reached base safely on the current play due to a fielder making an error during that play, not from a past play.

As far as earned runs charged to a pitcher in this situation

Rule 9.06 b) No run shall be earned when scored by a runner who reaches first base (1) on a hit or otherwise after his time at bat is prolonged by a muffed foul fly;