Update:
after two weeks and about 200 miles and almost daily drives, I have not had the tiniest stuttering since. None. Nothing. I made a very quick stop at the shop, where they measured fuel pressure, which read fine.

I really wonder what kind of gremlin was causing that heavy stuttering on that sinlge day and where it is hiding now...

 

Could be anything, from water in fuel to a loose connection, it’s running good now

 

Fuel is a common culprit, especially with the HHR 2.4. Many owners fail to notice 91 octane is recommended. With 87, when the motor sees load, knocking will ensue and the car will roll back the spark advance to protect itself. That typically causes hesitation at minimum. Alone that shouldn't cause the car to run too badly, but if it does, it can be unmasking other problems.

 

Update:
Shortly after my last update, the stuttering resurfaced. Interestingly during this period, the first 10 to 12 minutes of each drive were completely stutter-free. After that, the stuttering would inevitably commence. While under examination at the shop, the car would literally throw out black soot...

As the culprit wasn't 100% clear, we decided to first replace the upstream O2 sensor (GM GENUINE 2134537). And behold, the stuttering is all gone after having replaced the sensor. It didn't even stutter anymore with the old, soot-covered spark plugs still in place (now replaced with new ACDELCO 41103 plugs). We would have also replaced the downstream O2 sensor while at it. But it wouldn't come off and I didn't want to risk anything when not really necessary. So hopefully it's solved now with the gremlin chased away.

 

The #2 O2 sensor only monitors the health of the catalytic converter.
That explains P0171 and P0300.

 

Awesome! Keep it clean and drive it often!