prefix re as in rechercher, retrouver,

Bonjour Diana !

That's an interesting question :)

Technically, the prefix "re" does imply a repetition of a previous action, doing it again or back.
However, as you seem to have noticed, sometimes in French we will colloquially use either form of the verb regardless.
Je suis entré dans la pièce.
Je suis rentré dans la pièce.
-> You can colloquially use rentrer here, even though it's the first time you enter that room.

Now let's have a look at each case you mentioned:

grouper & regrouper

Here the meanings are different: grouper is to put objects together in a general manner, whereas regrouper implies the objects have been previously scattered, so need to be brought back together.

Same goes for trouver & retrouver : retrouver implies you previously lost it and found it again.

As for chercher & rechercher, their difference is in terms of context.
Chercher means to look for, whereas rechercher is more thorough - i.e. to research.

I hope that's helpful!
Bonne journée !