I believe your machine has a pump mounted external to the engine and driven from the front of the crankshaft.
Start by making certain the pump is being driven and the coupling mechanism has not come apart.
The HST is largely an independent system only needing a minimal amount of oil added by the hydraulic system.
This issue has to have more of a story. How long have you had the tractor?
Last time oil, filters and suction screen serviced and with Kubota products or other stuff?
Did this situation happen suddenly or has it been acting up before getting to this point?
Dave