How high can an aircraft fly?

I don’t know, I would guess they were ballistic. They used thrusters to maneuver when the control surfaces wouldn’t work.

The X-15 conducted both altitude and velocity tests. In the altitude tests it was operating primarily as a rocket with a reaction control system necessary at some altitude. By then the wings were no longer functioning as common foils anymore, they were just deflecting air downward in a 45 degree attitude.

Velocity tests maintained the airplane mode more of the time. The wings acted like foils and aerodynamic control surfaces were in use, and gaining maximum altitude wasn’t the goal of those tests.

The Karman line defines the point where the an aircraft would need to exceed orbital velocity for aerodynamic surfaces to work. I don’t think anything that could be considered “Today’s technology” could approach that line. If I understand it correctly (not the best bet you could place) existing rocket technology is a more efficient way to push an aircraft to orbital velocity at a much lower altitude and velocity.

It’s worth noting that the SR-71’s maiden flight was 54 years ago. Remarkable is an understatement.

They’re pushing for 90,000’ at the Perlan Project. In a glider, btw.

The core of air breathing self propelled hypersonic research is basically how to deal with very high stagnation temperature at hypersonic speeds.

Especially considering that that’s why supersonic combustion ramjets are needed., which have been perhaps the most central element to self propelled hypersonics research, and elusive to build, but now coming into hand as a technology. Scramjets would be the most fundamental difference between the combined turbine/subsonic combustion ramjet engines of the SR-71 and turbine/subsonic combustion/supersonic combustion ramjet engines on a projected SR-72. The main reason you couldn’t build an a/c with the SR-71’s technology that was a lot faster wasn’t necessarily skin heating, but how hot the intake air gets when you slow it down to subsonic speed for combustion, then raise the temperature further with combustion. The scramjet eases that restriction by allowing combustion with cooler supersonic flow.

Skin heating is also a real issue of course, but again some hypersonics research projects have been specifically to test new materials and techniques to make sustained hypersonic flight practical in term of leading edge heating.

In theory a scramjet-powered vehicle could sustain flight up to about 75 km (246,000 ft), this graph from STUDY OF AN AIR-BREATHING ENGINE FOR
HYPERSONIC FLIGHT, Author: Marta Marimon, September 2013:

Actual test vehicles using scramjets have flown briefly at 110,000 ft (33.5 km): NASA X-43 - Wikipedia

To take off from the ground would require a “combined cycle” engine which transitioned between turbojet, ramjet and scramjet mode. This was envisioned for the X-30 but was never built: Rockwell X-30 - Wikipedia

However ground-launched, scramjet-powered vehicles are still planned. The altitude would very with the mission need, but 75 km has been discussed as the theoretical upper limit of scramjet operation.

The Red Bull Stratos went to 39k.

I assume your units are meters?
From wiki:
" With a final altitude of 38,969 m (127,851 ft)* (23.3884 miles),"

Right. I assumed the OP meant heavier than air aircraft, that was a balloon, but I guess a balloon is a lighter than air aircraft.

The U2 climbed to 70,000 ft. and top speed at 500mph. The U2S is still in service.

Rex Kramer: [talking on the phone to the airport control tower] No, we can’t do that, the risk of a flame-out is too great. Keep 'em at 24,000. … No, feet.

The space shuttle isn’t an aircraft. It’s a brick with wings.