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The energy that makes you burn up is your own kinetic energy. The “small” deorbit burn slows you down just enough to touch the atmosphere, but you’re still going nearly full speed: 7200 m/s. Around 30,000 km/hr.
If you slow down more in space, so that you enter the atmosphere at low speed, you don’t burn up. But you need a whole lot more backpacks to handle the full speed. It’s cheaper and burns less gas if you use the air to slow down.
Rockets do not aim straight up when they are leaving. They go straight up for a few seconds, and then they tilt over in the desired direction to pickup speed.
They don’t burn up on the launch because they time the tilt over maneuver so that they get above nearly all of the atmosphere before they start picking up serious speed.