Let's hope your manager reads this book.
"The measure of success is not whether you have a tough problem to deal with, but whether it is the same problem you had last year."
- John Foster Dulles
This book at times brings the feeling of how we have a class of superhumans called managers that sometimes need to descend upon earth, down to the peon level and get involved in the trenches. This further brings visions of a pointy-haired boss who has no idea what is going on, but comes to micro-manage the plebs.
It's a classic "american" business book, where there's always an anonymous Steve or Alex that had a problem, but then he committed to reassessing or doing some crunches and now everybody is awesomely successful around Jennifer or John!
There's a lot of "common sense" advice, but it might be helpful to go through these things that hopefully already happen in your workplace.
Basically people want to be lead by people who also care about them. Trust and nurture, have 1on1's. Default to believe positive intent. Allow others shoulder the burden. You can always do things alone, but being a leader involves letting go and allowing a team to apply their talents for exponential impact.
People don't answer feedback and surveys because they don't know what happens afterwards and that anybody heard their feedback in the first place.
Provide a psychologically safe space for inclusion and truth. Invite to speak, make them understand their opinion matters. Don't say "just" your opinion. "Just" is belittling, every opinion matters. Tell people you're going to be wrong and you expect everybody to tell me when that happens and how we can make it better.
These kinds of things are always easier said than done. So, good luck.