Apple’s documentation suggests that the tasks are only run in the background, but in practice we’ve seen them running even when the app is in the foreground. But there’s no reliable way to predict when iOS will decide to run the tasks. Arc’s part of the process is to register the tasks then schedule them (in the sense of “I would like the task to run now” or “I want the task to run in an hour from now”). Beyond that it’s anyone’s guess. And Arc’s scheduling has little to no impact on how soon tasks get to run (asking for “immediately” is like wishing for the tooth fairy to be real, and “after an hour” isn’t much better).
Maybe very slightly. But the XR isn’t really all that old. It’s got a fairly recent CPU, with six cores, so is still quite powerful, and also has fairly decent battery life. My iPhone 11 also struggles to keep up with the various daily background tasks that need to run, even though I tend to get excellent battery life each day. So I think it’s more down to iOS just being very frugal about how much time it allots out to apps to run their scheduled tasks.
Aside: All of these background tasks that Arc needs to run are also registered as “needs power”, ie the task should only be run by iOS while the phone is plugged in to power. So that means that the task is explicitly not a burden to battery life, and shouldn’t be restricted on energy use grounds. But… that still doesn’t help with getting iOS to run the tasks more often or for longer. It’s a bit of a losing battle! 
Anyway, at least the next Arc release will take care of getting the monthly/yearly maps filled in. It might result in the occasional extra crash while viewing those maps, if iOS gets angry about too much CPU work being done. But that’s still better than waiting weeks before you can see the maps!