I agree with your second statement.
I suppose what I'm trying to vocalize is the following:
When working on code, the work itself is fun. Coding is enjoyable. That means an 8-10 hour day is largely 8-10 hours of enjoyment.
With management, those ~8-9 hours are no longer enjoyable. The end result is extremely fulfilling and meaningful, much more so than code... but I'm genuinely not finding the actual work of management enjoyable, quite the opposite.
I think I need a way to find the managerial aspect itself enjoyable, otherwise it feels like light suffering for several hours each day in return for the overall health of the rest of the team. And as much as I like these people, that's not long-term sustainable.
I think the way forward might be to fully commit to the positive aspect you highlighted. To consciously attempt to keep in mind the meaning and enjoyment that comes from the making of connections and improvements of the people around me.
I'd love it if a more experienced manager could chime in here and speak to whether or not that really can be enough to power one through the endless meetings, excel reports and politics given time.
And I agree with what other commenters have said. It is simply not possible to be a good manager, while attempting to stay relevant in technology. There simply isn't enough time each day for me to balance my life, keep up to date with code, and learn the management skills I need to improve on.
But that means consciously giving up on staying technically relevant, in this competitive industry..... for a new role which day to day, I'm not finding day-to-day enjoyable. That's a huge leap of faith, that quite honestly, I find very scary to take.
Meanwhile, it seems similarly risky to just give in and go back to pure code, and give up on this managerial aspect. I clearly do have an aptitude for it, it clearly is rewarding, and getting the opportunity to climb this high simply does not happen every day.
Hence, the feeling of being in need of advice, and somewhat stuck.