I wonder whether all species or even just one actually have a (shared) purpose? As humans couldn’t we all just try to find our own?

Not sure to understand what you mean here? Would you care to develop?

In a way we are just a very complex system

We are.

Life is very good at persevering but does that make it our purpose?

If I were to define them, I would separate life (as the yet-to-be-understood ‘force’ that make some things being alive), species (all the various kind of living things, arbitrary grouped and separated in categories by science), and the individuals (be it that plant on my desk, you, or I). I don’t think they all need to have a purpose, nor that this purpose is the same.

To me, life has no purpose beside maybe being what it is. Like fire has no purpose, it simply burns and converts some types of maters into light and energy (heat). At the very least, I cannot imagine life as a ‘conscious’ being wanting something. It just is a state of thing/fact (being alive) that science still can’t explain or reproduce.

Species on the other hand they all share a same purpose, which is to thrive as a whole (grow in numbers, but not too much in order not to endanger the very space they need to live in). At least that’s how I see it.

And then there are individuals. They may or may not have whatever purpose they fancy within a somewhat restrictive 'species limitation’.

I mean, as a butterfly I would not be able to live more than a few days no would I be able to mate with a whale, no matter how badly I would want it. And we, as humans, we may have managed to push our species limits way beyond what they were (we can fly, dive underwater, even go into space, we can also live much longer and if we still can’t mate with any other non-human species we do have learned to manipulate their genome, who knows where that could lead us?) but all of that is still very fragile and very limited (flying is a thing as long as we have access to enough energy and knowledge, we live longer but we all still have to die no matter what we try). So, within those boundaries set by what our species is, I would say we’re more or less free as individuals to be what we want to be. We’re less so in certain countries than others, and in certain times.

On the other hand, I have no idea what the idea of the individual could evoke in a bee’s mind? Or ‘personal desire’?

For me it would be to be a net positive to society in certain ways (that I’m not sure how to put into words and the bits I know how to could get long) before departing.

Imho, that is a very nice objective to pursue. No matter how you would manage to achieve that goal.