Outside of events, typically less than an hour/day.
Just long enough to pop in an reset 3hr production runs, and/or a few minutes here and there to do some tourny/spire.
During events, it depends. Obviously a lot more while the sequential quests are being chugged through, then down to just 'normal' daily play once it's the daily quests.
...or if I'm hobbying vs. playing on the Switch, I'll just leave my cities active while I work away on one of my too many 40k projects, whether it's Space Puppies, Angry Vampires, Stinky Marines, Dust Bins, S&M Elves and now, Orks. (yes, I have no life!
)