I'm not sure about stairs, but out on the trail the general rule of thumb for effort, expressed in terms of walking on the flat is distance + 13*elevation gain. So if you hiked 2 miles with 1000 ft elevation gain, the effort would be approximated as 2.0 + (13*1000)/5280 = 4.46 flat mile effort.
I would guess that your distance from doing pure stairs would be way off - stride length is probably about 12" whereas default walking stride from Fitbit is a bit less than 30" for an average height male, and if it thinks you are running (cadence greater than about 135) it credits you with an even longer stride ~ 36" (although this is not appropriate for jogging, which by definition is running with stride shorter than walking stride). Rounding, you have 4000 steps in 25 minutes, but at horizontal stair spacing ~ 12", real distance is more like 0.76 miles horizontal. Then presumably half your steps are up and half down. So 2000 steps up with typical 9" stair height = 1500 ft vertical gain = 3.69 flat mile effort.
Overall, 4.45 mile effort in 25 minutes, or the equivalent of running 10.7 mph on the flat. Seems doable but pretty hot! If you are doing stairs with landings, the total vertical is down maybe 20 or 30%, so perhaps the equivalent of around 8 mph on the flat. BMI also probably makes a difference - if you are a bit overweight it seems to increase the difficulty while climbing much more than it does on the flat. And conversely if you are a bit underweight . . .
Hope that helps.
