What about natural healing of not-resting Creatures?

[Eru_Iluvatar]

According to the rules, "With a full night’s rest (8 hours of sleep or more), you recover 1 hit point per character level. Any significant interruption during your rest prevents you from healing that night.", but some Types, like Plants or Oozes, do not rest: does it mean they are prevented from healing by the passing of time?

Constructs and Undead with no Intelligence cannot heal themselves, but no such clauses are written in the list of Plants', Oozes' or other not-resting Creatures' traits.

[TxSam88]

as they are monsters, the GM can have them heal however much he wants.

[Mysterious Stranger]

You did not read the next sentence.

If you undergo complete bed rest for an entire day and night, you recover twice your character level in hit points.

There is no requirement that a creature undergoing complete bed rest has to be sleeping. Plants and oozes often completely still for long periods of time. A plant or ooze that remains completely motionless would be able to heal from bed rest.

[Azothath]

it's laid out in the CRB or on AoN, or in short restated in -->UltCmbt<--. In general a creature is Active(conscious and walking about, eating & drinking, fighting(combat) or "strenuous activity", forced march, playing instruments, crafting items, etc) or Resting(sleeping, inactive, "bed rest", and/or unconscious, then 24hr bed rest with/without care). A creature could be time stopped/stasis/petrified/treated as if dead but that's rare (mainly spell effects).

RAW is written in common american english from a PC's(GMs) point of view as the GM has to run the Game. GMs usually play fair unless they need to make a dramatic point (it's Story Time!).