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.
It seems difficult to have enough bottled oxygen to deorbit yourself, but maybe doable.
The MMU backpack units on the space shuttle had a total delta v of ~30 m/s. You need about three times that amount to deorbit from ISS. So imagine you need 3 MMUs give it take worth of expendable propellant oxygen, and you can do it. (The MMUs used nitrogen, but for this purpose oxygen is pretty much the same.)
After you deorbit, you will of course burn up on re-entry with no heat shield. But it might be conceivable to design a personal heat shield surfboard.
You could also avoid the whole burning up things by braking a lot more during the deorbit maneuver. But instead of 100 m/s, you need to slow down by more than 7000 m/s. That’s quite a few more MMUs worth of gas. But if you do that, then you’re essentially making a free fall jump from space, which has more or less already been demonstrated.
Edit:
To address the linked article in some way: each astronaut on the station has a dedicated seat on a capsule to come back down in an emergency. Usually, it’s the same space capsule you came up on, but not always. Those are maintained ready to go at all times, and the astronauts can be back on the ground in 60 minutes whenever they need to. These spacecraft can be operated to splashdown by astronauts alone with no ground assistance, if needed.
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.