Task, team, individual
No wrong answers here except ignoring one or two of these. Every EM has a preference. One of the things you want to find out when interviewing EMs is when the chips are down, does the candidate index highest on task, team or individuals. Case studies can be really good here.
Tech, people, systems
Too much tech is an obvious red flag... unless it's a tiny org that really doesn't need an EM yet. Some orgs create roles where the tech is entirely out of the equation, and the EM is a pure manager of people. Even then, time should be allocated for systems of hiring, people management, review cadences, performance criteria.
Now, next, later
This is often situational. One trap is staying focused on the Now once the incident is solved, the last minute report is done, the spend is back under budget. Another trap is obsession with later at the expense of next. Some time for long term vision is essential, however it's the next that will move the needle, and stacking a few solid quarters together under a loose vision often works a lot better - and is appreciated much more by the business - than looseness on the quarterly level with a strong but always further-out vision.
Ground level, tree tops, mountain top
More traps here. Punting the ground level to your seniors and leads can work if you've developed high trust. I've worked with a few leaders who refused to leave the mountain top... I've never seen that work long-term. The only way I've seen it work is when EM is a quick stop on the way to higher rungs, directorship or beyond. Stick in the EM role for a year or more without at least coming down from the mountain and at best you'll have a team that nods along but isn't listening to half the words you say.
Working in the org vs working on the org
The EM who takes an on-call shift or puts in a toil PR understands the pain of poorly constructed systems or flaky CI. Not to mention winning the respect of their team. Especially relevant for new EMs coming into an org. A lead who's been there, done that and has their name all over the blame might be able to get away with spending full time working on the org... if they can resist the temptation.