Ozan, overall I see some good things going on in your skiing, and honestly, I'd be quite happy with myself if I could do as well. A good aspect of your skiing is your ability to develop some strong hip angulation and separation. (Agreeing with Mike King.) That should be a good foundation to build upon.
In the medium radius turns, you create a smooth and relaxed appearance. I like that you are generally initiating turns without pivoting flat skis. Where I think you could do some work is in the latter part of the shaping phase and in the finish phase. Particularly on the steeper parts of the hill, you consistently stop the turning action in the latter part of a turn. Your runs have substantial sections where the skis are traveling straight between turns. I think that you could make your skiing more versatile and dynamic if you could achieve a continuation of the turning action right up to the point at which you go into the transition into turning the other way. As you approach the transition, you are losing the upper-lower body separation (as Mike King noted). I see this as being a result of you getting static in the middle of the turn. I'm not seeing a continuation of foot tipping, angulation, and separation as the turn progresses. Remember that these are MOVEMENTS, not positions. They should develop progressively through the turn (advice the geepers already gave). It might help to be cautious about not using up your range of motion for angulation and separation right in the initiation phase of the turn. You'll need to have some range of motion in reserve for later.
On occasion your inside foot abruptly shuffles forward relative to the outside foot, and you develop an excessive tip lead. (Karlo noted this.) This brings your balance to the inside, leading to you losing your fore-aft centered balance on the outside ski (the outside foot "drifting aft," as Mike King put it), and leading to the tails sometimes slipping out. As Mike King and geepers said, you should seek CENTERED balance rather than FORWARD balance, and it may even move to the back as the turn progresses. Beginners and novices are always too far back, with vertical shins, so everyone gets it drilled into them that they need to get forward, but the result is that better skiers often overdo it.
Improvements in these areas would set you up better for the transition to the new turn. A very dynamic way of initiating is to minimize the vertical extension that you're now displaying (and you've noted), and instead seek to bring the skis up under you by continuing the skis' turning action while maintaining a well-centered balance (fore-aft), and flexing the old outside leg. This will lead to the support for your body mass being withdrawn, and your mass starting to topple down the mountain. This will give you the opportunity to begin tipping your feet over into the new turn and create very early edge angles, while your skis are still traveling across the fall line.
Your current pattern of vertical extension creates slow transitions. If you strive to create quickness in the movements leading from one turn to another, it will give you the opportunity to make your skiing more dynamic. The speed at which you're skiing in the video is more than adequate to make a "pop" unnecessary.
Honestly, it's difficult to see in the less focused parts of the video, but I think there's a likelihood that your pole touches are misdirected, reinforcing you moving vertically and bringing your balance briefly too far forward. (But on the lower parts of the runs, pole touches were often absent.)
In your short radius turns, I see you starting the turning action on a flat ski. Expanding on what Mike King said in perceptive detail--your vertical rise in transition leads to you bringing your balance point forward. As a result, the tails of the skis skid out. This is followed by a bit of a hard landing. The turn radius is not consistent. In that spring snow, you get a big spray from the skis, all happening in a brief portion of the turn. I think the pathway to improvement is going to be similar to what's needed in medium radius turns--it will just take even greater focus and precision in putting the skis in a place where they will perform for you. Your 15 meter skis should be capable of making some nice carvy short radius turns.