I have not seen such options in the F-18C (DCS version) or in any of the other military aircraft that I have flown in simulations. The only option you typically have is to fly to the desired altitude and then hit BALT or RALT, which engages the barometric or radar altimeter altitude hold function.
Not sure why they don’t have the autopilot options you mention, but a fighter aircraft is surely flown in a different way then an airliner. The climb is typically much shorter than that of an airliner, the climb rates are insane . Perhaps the relatively short climb reduces the need for autopilot functionality?
Also often they fly in formation, with one of the planes in the lead, and the rest just follows. It is probably not desirable to fly on autopilot during a formation flying climb.