Generally, I think sending a 3 if the school gives credit (or higher placement) for the test is ok. BUT there are highly rejective schools were I wouldn’t do that, for example if one were OOS for Ga Tech or UNC Chapel Hill, I wouldn’t send a 3 (or lower) even though these two schools do give credit/placement for some 3s.
Generally, even highly rejective schools are looking for reasons to admit, they aren’t looking for reasons to deny. I personally don’t think a 4 would be directly responsible for a denial at many schools. With that said, I could argue both sides of the decision to send/not send a 4 in a major related area to highly rejective schools, so I leave that up to you. If you are proud of the score, send it. I would encourage you to send a 4 to all colleges on your list that aren’t highly rejective.
Most colleges allow self-reporting of the AP scores, so don’t pay to send those unless you must. If you want credit at the school you do enroll at, you will have to pay to send the official scores at that point. Good luck.