They only appear in DA/TA, not in the base game, IIRC.

They were far more common in DA compared to TA. Maybe 1% of all worlds will be under PQ4 in TA, not counting whatever race it is whose second home system planet is always PQ3.

Way back in DL, you could abandon planets and only suffer a PQ loss of 2. It was possible to repeatedly abandon colonies and recolonize until the planet became a PQ 0 planet. For most players, abandoning colonies wasn't very useful or productive so I imagine that few players from back then would know about this.

By the way, there was a change in the game a while back so now abandoning colonies will reduce the PQ to 0, so there is little point in trying it out for yourself.

I have come across it in DL... after a really long gigantic game, the Terrans found a precursor technology that increased the PQ of all uninhabited worlds within three secotrs by 3... which raised all the PQ0 planets up to PQ3. pretty awesome!

You only found one? In DA the AI won't colonize PQ1 planets at all, so you can colonize them long after the colony rush is over.