Manage risks, not methods.
The hardest part of transitioning into management is becoming comfortable with people doing things differently from you. Your job shifts from what you can output to how much output you can generate in others. Many first-time managers make the mistake of thinking their job is to ensure their reports do exactly what they would have done.
When you become a manager, you may feel that the people you manage won't do things as well as you would have. This is often just ego. You need to recalibrate. No matter how good you are individually, you won't outperform a team of great people.
You might be tempted to create your own personal 'playbook'. This playbook exists –probably only in your head–to teach others to replicate your behaviour. If you do this, your feedback will become about the method, regardless of the outcomes. You'll get frustrated because people think and act differently from you. Your team members will get frustrated because your feedback is about how things were done, not what they created.
Ultimately, you need to focus on outcomes. If the work gets done, the goals are achieved, and the budget is met, then how it happened shouldn't matter. This is a great thought and true enough in the abstract sense, but waiting until there's an outcome to give feedback is likely too late. If the project is a flop or runs well over budget, you won't get much forgiveness from your own manager.
Instead, you should work on helping your team see, weigh, and address risks to give helpful feedback and minimise the chance of things blowing up. Finding risks and classifying their likelihood and impact takes practice. It can feel tedious and silly in the beginning. Lots of identified risks can probably go without saying. You don't need to put together an ISO9000-compliant risk register; a lot of this process can be done on vibes in almost all cases. Flag something, write it down and decide whether it's a risk you want to take. That's it. I am not one to recommend a process just for the process's sake.
You can manage some risks through policy or rules of thumb. When people know the principles by which your team operates, they can better self-select risk. More junior employees should take more minor risks. Your job as their manager is to allow them to expose themselves to a level of risk aligned with their capability to handle both the mitigation needed and the outcome should it occur.
You need to let your team own the risks they choose to take. They need to feel materially attached to the positive and negative outcomes. You shouldn't make any negative outcome existential, but don't absolve them of any responsibility just because the risk was identified. Conversely, by agreeing on the risks, their impact, and the probability of occurrence, you need to be comfortable with a 1 in 10 risk happening 1 in 10 times.
You'll need to learn to calibrate yourself, your staff and your organisation. One way to do this is to keep a risk prediction log. Check back over time that events you claim are 1 in 100 happen roughly 1% of the time. Calibrate both frequency and severity. You can only do this if you predict and record in advance. With the hindsight of 'I knew this would happen', everything is perfect. Again, it doesn't need to be exhaustive. Lower frequency risk will need more samples to calibrate against. That's fine because they're unlikely anyway, and if a 1 in 1000 is a 1 in 10, you'll find out pretty fast.
If you switch from criticizing method and instead help ensure you and your team have a similar bias for risks, managing them will be easier and far more rewarding.