every shot in tennis should be built, from the hand down to the ground. in the REVERSE sequence of the K chain.
therefore, the core rotation being relatively early in the chain, should be worried about later in the build.
OP seems to be well coordinated, perhaps this is not even an issue.
so in the sequence of from the hand down to the ground:
grip - check;
wrist flexion - maybe an issue, maybe not, let's park it.
elbow/shoulder area - as I pointed out this is the biggest issue, right now.... watch that video about the power loop, this should fix the wrist flexion..... because right now your racket going straight up... this causes the lack of an angle between the handle and the forearm at impact.... also causes the momentum to bring the head straight down after impact, causing excessive wrist flexion.... if you power loop from the outside, the racket will come inside for the impact, the going outside again during the follow thru.
as you drive up from the ground and the hips/core rotate, the racket should NOT sink deeper into the back scratch by stretching the triceps. your motion aint too bad, but is still too much inside compared to the pros. the loading should be the power loop to the outside causing the shoulder to rotate externally, the so called ESR loading.
now we can talk about rotation a little. when the above is fixed, the rotation will likely resolve itself, as now the rotation will have the correct purpose.
the other benefit of the power loop, or the out-in-out swing path, is that there is a lot of speed from the pronation, the racket flips quickly from left to right. the result is you may be less accurate on the direction, but more accurate on depth... this will likely help on your scattered landing patter, as a straight up then down swing path you have right now has the racket face going from extremely open to extremely shut very fast, making it difficult to control depth.
the service box is painted longer on the depth than width, but the actual landing area is much more forgiving on the width side, there is only a narrow strip depth wise between hitting long and hitting into the net.... so the loop swing, to some extent, takes advantage of the actual shape of the valid landing area.
so to summarize - fixed the arm/shoulder swing path first.