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I have left a link to the NASA video in case you are not to sure what I am referring to or to get a better picture of what I am talking about.
https://www.youtube.com/watch?v=bnKFaAS30X8
With that in mind, I imagine that some of these planets if not all would be capable of having sentient life.
Question: How would these sentient species play a role on each other's evolution/growth?
It would be extremely unlikely for two (or more) civilizations to find themselves at the same level of technological development. What is likely is that some civilizations in that system would predate others by millions of years.
Given that consideration, things could develop in following ways:
Colonization. The eldest civilization fully colonizes other worlds, giving them no chance of developing their own civilizations.
Cohabitation. Eldest civilization colonizes other worlds while indigenous species continue to evolve, finally becoming sentient on their own.
Grooming. Eldest civilization deliberately directs evolution on other worlds to produce sentient beings.
Seeding. Eldest civilization does not colonize other worlds, or withdraws from them after a while. However, other worlds would still be populated with a number of species from elder civilization's world, eventually evolving into sentient beings, maybe similar to "elders".
Isolation. Eldest civilization maintains isolation of other worlds. Eventually they also may become civilized ones on their own.
The above ideas about multiple civilizations imply that life has a high chance of developing an intellect, which may not be the case.
The only sharing of life between these planets might be microbes. There's a theory that comet strikes could fling microbes out into space to potentially seed other planets. Unproven so far. But we don't see any higher lifeforms traversing space, and the question hasn't proposed any of these aliens have that ability.
Beyond that, there's no interaction while the species are evolving, so the answer to your question "How would these sentient species play a role on each other's evolution/growth?" is "They would not play any role in each other's evolution/growth."
If the question is meant to be about their cultural interaction as mature species, that question is too broad to be answered here -- it encompasses the entirety of speculative fiction on aliens!
Whooo (like halting a horse) there, "With that in mind, I imagine that some of these planets if not all would be capable of having sentient life." While one or possibly more of these planets may be the best chance of finding life on a different world finding intelligent life is a totally different situation. In only one instance has intelligent life here on Earth been proven on a world filled with life for millions of years. (Yes there is a questions whether we can classify dolphins, whales or even some apes as intelligent but for now we will stick to humans because we are the only ones capable of leaving the planet at the moment unless of course we take some of the others.) While some people think life on Earth may have arose from life on Mars or from elsewhere in the universe via extremophiles we do not know if panspermia (the name some scientist have given to that theory) will actually work or not. I will be thrilled to find some sign of life one one of these planets. I am not sure about sentient life. At only 40 light years if it were less advanced than us I would be concerned about our future effect on them. If it is more advanced than us I would be terrified of what they would do to us when not if they discovered we are here!
Assuming that all of the planets are inhabited by life, here's what I'd see as the most likely situation.
The first space faring civilization would completely control and dominate the system without any other sentient races in the picture.
Life emerged on earth 4.1 billion years ago. The first evidence of tool use dates back 2.5 million years. We first went to space 56 years ago.
Extrapolating from the only example we have - very soon after life evolves to the point of general intelligence and tool use, we progress to a stage where interplanetary colonization is possible. When the first species to develop space flight goes to visit these other life-bearing worlds they wouldn't even find basic civilization, because if any other world had progressed as far as tool use first they would have already colonized the others.
Hope this helps!
