I have found that Shimano offers non-series road flatbar shifters such as the 11-spd SL-RS700.
So this one can be used with GRX-derailleurs, as GRX is compatible to all roadbike components Shimano offers.
The original source (in German) is here : https://www.mtb-news.de/forum/t/shimano-grx-schaltwerk-flatbar-schalthebel.908787/
I'd go with XT 11 speed shifter and derailleur. Shimano does not publish MTB-Road groupset cross compatibility and I'd assume GRX and XT are not compatible.
I think a bigger issue is whether a GRX crank is compatible with your bike.
GRX cranks are designed to fit road-like gravel bike frames which may have a narrower bottom bracket than MTB frames. If you ...
https://www.sjscycles.co.uk/gear-spares/shimano-duraace-st9000-name-plate-fixing-screws-right-hand-y63x98020/ says that Y63X98020 is a name plate for the right hand lever of a ST-9000 brifter.
A review on that link says:
unfortunately I mistakenly ordered st9000 I returned for credit and ordered the correct st9001 very happy
So from that I conclude ...
Specifically addressing the second of your suggestions
split bars with shifter next to the stem
This is a bad idea and would strongly recommend against it.
The GMC Denali uses this method in order to fit grip shifters to a dropbar.
The dropbar has been cut through in the middle, allowing the maker to fit the twist or grip shifters. These will be ...
Shimano and SRAM cassettes of the same speeds (up to 11 speed) are all basically compatible with each other. The overall cassette width and individual sprocket widths and spacings are standardized for each number of speeds.
(This does not mean you can use any 10 size speed cassette in a drivetrain of course, as the derailleur has to be able to handle the ...
All signs point to yes. The differences between 10 speed chain width and 11 speed chain width are minimal (5.88mm vs 5.62mm) and although the spacing on the cassette is narrower for 11 speed the front chainring spacing is often the same.
Lennard Zinn says it'll be fine