The simple common characteristics of great engineering managers
The single most important characteristic a good manager will possess is the ability to decide on a course of action and communicate it to the team. When this happens, a manager becomes a leader, with a team who can follow their direction. Arguably, this doesn't even have to be a correct course of action, because even a bad but well-defined one will give the team practice in working together toward a goal. Without a manager's clearly defined direction, the team is rudderless, and anything positive that comes out of a team is due to the team members' own characteristics, not anything the manager did.
The next most important characteristic is, naturally, for the manager to know why they're choosing this course of action and for their reasoning to be correct. The why will change depending on the context; it may be to ship some product quickly, or reduce costs, or help with recruiting, or even something as simple as it'll make their team look good. If the first point is "did we set a goal?" this second point is understanding why we set that goal.
Next, the manager must be able to communicate that goal to the team. I've seen countless managers fail not because they had poor direction or poor decision-making, but because they could not actually communicate any of those things in their head out to their teams. They understood what they wanted - no one else did.
And this is important enough for a sidebar: communication isn't just about one person sending a clear message, it's also about the listener receiving it. I could give a cogent set of directions to someone in classical Greek, even expressing computer science concepts, but no one would be able to do anything with that unless they also spoke classical Greek. Even when we're both speaking English, communication barriers can get thrown up because of lack of context, lack of trust, stress, distraction, or any number of seemingly minor factors. Part of a manager's ability to communicate is the ability to detect these barriers and work around them.
The next most important characteristic of a manager is to communicate how that goal helps each member of the team, personally, individually. Some things are so obvious they don't need to be stated ("this is part of your regular job description and why we hired you"), some need a little more exposition ("this helps grow the company, which means we can afford to pay you more money"), and some may need a lot of directness ("this is actually a project that will lead to your promotion"). Not every goal is going to bring about a substantial change in someone's life. Most will be building blocks. It's important for a manager to help stack those building blocks over time.
Finally, and least important of all, is the ability to lay out the team's operations for how they will meet a goal. The manager needs to be able to do this in order to understand the team's day-to-day behavior and activities is progressing toward a goal. If they don't have a firm understanding of how they might do it themselves, they're in no position to audit the team's activities. In general, though, it's bad practice for a manager to actually micromanage day-to-day activity. It's frustrating for smart people, and it removes the opportunity for those smart people to actually find a better way to do something. A manager still needs to have a sense of how the work is to be done.
Typically, when people get frustrated with their boss's boss, or their boss's boss's boss, it's because that person has become detached from the actual work, and their strategies no longer align with operational reality. I listened to a podcast with Jamie Foxx where he lamented no longer being as funny once he got famous. He was still the same Jamie Foxx, just no longer in the same context where he used to get his jokes. The same thing happens to leaders as they accrue more responsibility. Great strategic leaders will cope with this in several ways: they get really good at hiring people who are tuned in to the reality on the ground, and they trust them; or they periodically dive into the details themselves to understand what they might be missing.
Beyond these points, most other characteristics of great leaders are subjective. There are profiles of great leaders who were incredibly kind and warm-hearted, and other great leaders who were distant from their reports. Fred Rogers was known to be just as warm and caring with his team as he was on set, while Steve Jobs was famously mercurial. Some great leaders had highly collaborative styles, some were more dictatorial. Some were charismatic, others generally unlikable at parties. The unifying characteristics of those that succeeded 1) had a vision, 2) understood that vision themselves, 3) communicated that vision well, 4) showed people how it would help them, and 5) continually ensured that their vision was turning into reality through operations. The rest is preference.