I would say it is possible to use it with almost any adjective (tout petit, tout beau, etc…) but in my mind using it implies some sort of affection, and denotes a sense of endearment towards the thing being described.

A bit like using ‘wee’ in English: un tout petit bébé -> a wee baby

I do not think there is an actual rule for it.

There is no specific rule defining the use of “tout” instead of “très”.
It is mostly an oral use adding an undertone.
For example, “un très petit bébé” in a french’s mouth means that an usually small baby. “un tout petit bébé” means a cute baby.
Sometimes the undertone is friendship, cuteness, humour …
If you use “très” to mean “very” in some cases, your friend might not react as expected.

Keep in mind : “tout + adj” does not mean “très” in every cases.
“La salle est toute bleue” : means the (almost) only color of the room is blue.