I'm running a slightly different setup but I figured this might be useful info. I have a silver2 shifter in a riv thumb shifter mount on my 1x11 Susie. Shifts through the range easily. I would switch that 9 speed shimano shifter in your photo into friction mode and test if it'll shift through that 11 speed cassette. My guess is that it will. If you want 11 speed indexing, that's a different story.
Specifically regarding microshift shifters, some (maybe all?) of there shifters are physically bigger than the 9 speed shimano shifter in your photo. So some material would need to be removed from the bar end pod to simply fit the shifter in there. But this has to do with the physical dimensions of the shifter, not the shift range.
I guess I need some clarification with one thing related to this topic. Is there a difference in overall cassette width when comparing, say, a 9 speed cassette and an 11 speed cassette? Seems to me that any cassette designed for an HG freehub body would be constrained to the same outer width (distance from smallest cog to biggest). As my understanding goes, the jump from 9 speed to 10 or 11 is achieved with a narrower chain and reduced spacing between adjacent cogs.
Hope this was helpful in some way.
Matt