I am putting drop bars on one of my MTB Shimano 10 speed 1x Deore. I am looking for a road hydro shift lever
The only road shifter compatible with a Shimano 10 mountain RD is the Microshift BS-M10.
If you went BS-M10 you could use TRP Hylex brakes to stay hydro.
A number of bikes have been released with those exact components with Shimano 1x10 or 2x10 mountain drivetrains. It works fine if you're amenable to bar ends.
Other than the above, to get 1x10 with brifters and hydro and re-use your RD, all the options are seriously contrived, like buying the 1x11 hydro GRX STIs only to also buy a Jtek for them. Apex 1ing the bike will be cheaper.