I can confirm that this really is an issue and has made me barely play this years game and I've played this game every single year since before it was even called Football Manger.
I don't have much time at the moment but here's what I have found so far with my main goal being to have on my profile page saying the following.
Tactical style- Vertical Tiki Taka
Playing mentality - Adventourous
Pressing style - Often
Best I could do was
Tactical style- Vertical Tiki Taka
Playing mentality - Balanced
Pressing style - Balanced
To compare Xabi Alonso looks like
Tactical style- Vertical Tiki Taka
Playing mentality - Attacking
Pressing style - Often
After 50+ reloads trying to find the perfect combination of formation 4231+433, passing directness, tempo, width etc... I found the only way for it to say Vertical Tiki Taka is on the balanced mentality. much shorter passing and higher tempo (default vertical tiki taka doesnt even work, comes up as control possession I think) Increasing to positive or attacking will end up being tiki taka, control possesion or gegenpress. FM23 is not like this. I loaded up FM23, play 1 friendly on positive, save, load into FM24, profile says Vertical Tiki Taka, play 1 more friendly and it changes.
Also staff search
Control possession 22 Found
gegenpress 2
tiki taka 3
wing play 30
vertical tiki taka 2
Sorry for the badly worded post, but I have to go now.