Velocicraptor, I'm curious what front foil wing you are riding on?
Here's what I'll add. This is a short clip of some my very first more successful toe-to-heelside tacks back in Dec of 2019. Not pretty but I got them around. The foil wing I was on was a Gong Pro XL (1900 sq cm!). Also on an original Duotone wing and big ole Blue Planet 5'8"/114 L board (sure seems like ancient times now

). One of the key factors to readily staying up on foil throughout the tack for me was what I call "corkscrew" progression of your turn. Even now after a gazillion additional tacks (both heel and toe side) and 360's since then, I still do a bit of a corkscrew progression.
Like the previous posters have said you definitely go into the tack with speed but don't get overly hung up on high speed as the key to success. In this early video I'm not really going all that fast. My tack starts out as a traditional "carve" turn but as I head into the eye of the wind it changes quickly to much more of a quick "pivot" turn where I use my legs to "push" the board through the rest of the turn quickly, hence the "corkscrew" term. The problem in watching a video is that it's hard to tell between general carving and when someone is using their legs to pivot turn. Anyway, this gets you through the eye of the wind on foil quickly,.but of course you need to roll the wing quickly and be ready to regrab quickly in order to stay on foil because you've lost a lot of speed at the end of the turn. I'm not a mad pumper so I rely more on that pivot finish with a quick regrab. I think a decent size front foil gives you a bit more leeway before it stalls at that critical regrab moment when your learning your tacks.
FWIW , every time I try and learn a new move by being super aggressive with speed and rapid hard carving, I fail miserably. I need to be aggressive, BUT methodically smooth to make it work. If I rush anything I fail. For the harder heel-to-toeside tacks and 360's that's even more the case.
Yesterday I finally started up again on my behind-the-back tacks (did a few of them last year) and always had to "smooth" myself out to get them close to working. Good luck!