Well, I have to disagree. I very much doubt that Koeman isn't instructing his players on how to make synchronized runs. That is something any coach managing U14+ will be telling his players.
How well a team does this depends much more on the particular culture and atmosphere pervading the squad. We've cultivated a culture dominated by the attitude of 'don't bother making those runs because it probably won't lead to anything'.
I think that a coach has the ability to influence it by way of shocks to the system, instituting something radical that shakes up the natural status quo order of the team. But just instructing your players to do something won't really do anything. Remember that half time speech footage of Valverde beseeching the team to increase the intensity? We still went out there any game with less intensity than any other top team in Europe. It's about team mental culture first and foremost.
This attitude we have is one that players internalize quickly and then start to propogate themselves with their body language. It becomes entrenched, self-perpetuating. With Pedri you get players who naturally default to the culture of the team. He's not really a guy that seeks to change this attitude. Someone like Frenkie, you could see pushing the squad to break their comfort zone. Coutinho did it for the first few months here but then succumbed to the complacency.
That's the nature of this thing. A positive team culture needs to be reinforced mutually, collectively. If player X starts making runs that call for a synchronized pattern to engage, and no-one else follows his lead, very soon that player X will stop making those runs too. Then when the next new signing Y arrives, player X will likely be one of those dissuading Y from making the same runs. What you need in this case is less subservient and more renegade players. That's why I don't think Pedri will change much. Yeah he's brilliant and calm and all that but as a team, we have bigger problems. (Maybe some of them will dissipate once Messi stops, that's another conversation).
Your whole post is about Pedri doesn't dribble. It is true that he didn't do it last season. But this was from many factors. Maybe due to not being 100% fit, maybe from coach's tactic. He was different in his first months here when he played with flairs.
Things are different in Euro. Who made most carries in final third in Euro??? Pedri. Who made most passes in final third??? Pedri. Who made most through ball??? Pedri. Who had highest xG action??? Pedri.
Conclusion: It depends on how the team, the coach wants from him.