Simple way to group the list-indices of equal elements?

I would do it like this

Values[PositionIndex[list]]

You can use the ResourceFunction GroupByList to do this:

list = {1, 2, 3, 3};
ResourceFunction["GroupByList"][Range @ Length @ list, list]

<|1 -> {1}, 2 -> {2}, 3 -> {3, 4}|>

list = {f, f, g, g, f};
ResourceFunction["GroupByList"][Range @ Length @ list, list]

<|f -> {1, 2, 5}, g -> {3, 4}|>

Use Values to convert the Association to a list.

You can also used Reap/Sow, e.g.

pi[u_] := Reap[MapIndexed[Sow[#2[[1]], #1] &, u]][[2]]

So pi[{f, f, g, g, f}] yields

{{1, 2, 5}, {3, 4}}