A few meta-notes:
A manager is a coach. That's it. Having been a good player can be very helpful, but that's not the job. It's also not about being the boss. If you have to tell people what to do at every step, that means they're not playing well, which means you're not coaching the team well.
A coach does two things:
Those of course break down into hundreds of action items, but ultimately everything a coach does should contribute to one of those two categories.
For the team to be focused on the vision, they have to know what it is. And that makes communication a critical skill. Specifically, this means:
Distill everything important (vision, processes, goals, etc.) into memorable phrases that encapsulate the whole idea in a few words. There's a great Eugene Wei essay about Jeff Bezos's knack for this: "one of his great strengths as a communicator was the ability to encode the most important strategies for Amazon in very concise and memorable forms." That's where ideas that have become popular outside Amazon like "Day 1" and "disagree and commit" come from.
You need a team vernacular. Catch phrases, mantras, behaviors, etc. I had the good luck to get to see this up close from coaches Biff Poggi and Joe Ehrmann when I was a 14-year-old equipment manager (read: water boy) for my high school football team. Poggi and Ehrmann were local juggernauts in the high school football world, both well on the way to becoming fairly well-known in the high school coaching world nationally. They remain two of the most effective leaders I've ever gotten to see work.
I still remember the team's goal, because they said it at damn near every practice and made us shout it back: "Win the league and beat McDonough." I still remember how they said we'd get there: "50 guys loving each other can't be beat." And there were maybe eight more of those. And, critically, they modeled those ideas dozens of times a day. Touchstones where a short phrase stands for "load into your mind the hundreds of hours of corollary knowledge that you've gotten from executing on this phrase".
So you've got your vernacular. Now you need to repeat those ideas constantly, forever. Culture is the things you do and say frequently. If you say it once a quarter at your all-hands, that's not culture, and that's not the team's vision. That's just a thing you said a couple times that nobody remembers.