I ended up as part of a team managing the internal communication & knowledge platform for a company that was at the time (early 2020) about ~100,000 employees, now ~146,000. My area of responsibility now includes over 20,000 employees, but I do not directly oversee anyone. I did not have education or much experience particular to this domain, but somehow became a preferred pick for the role, so make of that what you will.
The strategy I've always tried to employ is to treat everyone as intelligent equals, and making as much effort as possible to understand, and earnestly explain, the way things are "supposed" to work in a bureaucratic perspective — who needs to approve, what process needs to be followed, while at the same time consciously addressing instances where what people want/need might be different, and that bureaucracies must be understood in that context. In other words, be aware of the Chesterton's fence principle, but also be aware that taking down the fence is an option that may need to be discussed.
The most common... I don't want to say "obstacle" because that feels so strong, but the thing I most often have to be consciously aware of, is getting the input of everyone whose input should be included. You have to actively seek it out, and push people to give input. It's never because anyone feels "silenced" or anything like that, it's more often that people just feel too busy, or feel their insight isn't important enough, or is not different enough, or wouldn't matter anyway. Voter turnout problems, now that I think about it.
These two talks cover a lot more in ways I think are really useful:
https://www.youtube.com/watch?v=mkLGLKcplkM — Concrete Practices to Be a Better Leader: Framing & Intention
https://www.youtube.com/watch?v=-zRaFJHK0S4 — Game Studio Management: Making It Great
There's also a little anecdote, by Adam Savage, talking about Michael Stevens, that I can't find (it's somewhere in his Q&A videos on the Tested channel), so I won't try to directly quote it. Adam was talking about asking Michael how he manages to stay so respectful of people, even when telling them things they don't know, and Michael answered something like "Overestimate their intelligence, underestimate their vocabulary."