Every Shimano hydraulic brake uses mineral oil. The material used for the seals is known to be incompatible with DOT brake fluid so I suspect using conventional grease may have caused the seals to swell irreversibly.
You should never need to grease the pistons of any bicycle hydraulic brake, since the fluid is a lubricant and the pressure seals so tight that they would wipe grease off the piston as it retracts. Grease may also become less viscous when heated, allowing it to drip onto your rotor with catastrophic effects, or may catch fire.
In future, you can use spacers and clamps to restrict the free piston so all the pressure goes to the sticky piston. Ensure the piston doesn't move so far that it leaves the seal. Clean with brake fluid and a soft cloth or q-tip. Push back in and retest. If cleaning isn't enough, the piston's seal surface, the seal or the caliper may be damaged, or one fluid passage inside the caliper could be blocked. Such issues are rarely user-serviceable.
Shimano uses easily-damaged ceramic pistons in its XTR brakes, I'm not sure whether any XT models also have them. Ceramic pistons are definitely Service Center only.