(In this answer, I'll try to focus on the power armor and the immediate ramifications of its widespread availability. There are other setting elements that will have a much bigger impact, but I'll consider them out of scope for the question.)
The power armor itself would not change much
In a society that has interstellar travel and general purpose AI, there are far worse threats than even a reaction-boosted, power armored, AI-assisted human. You are merely "upgrading" people to a level where they can hope to withstand the stresses of extended space travel.
A useful thought experiment for the military viability of any kind of manned vehicle (power armor counts) is to replace the squishy human inside entirely and see what would change. Except for the speeding up of thoughts, all the benefits of your power armor (protection, mobility, AI assisted aim) are things that the suit has without its wearer. Current day active defense systems have reaction times in the milli- to microsecond range. That's difficult to beat, even for a heavily augmented human. So unless your "time dilating" organ has incredible, physics-defying powers, you can build a strictly better combatant by just leaving the human out.
It might, however, mean that humans are able to participate in "infantry scale" combat. Since interstellar travel takes a long time and people wearing power armor are readily available, it seems plausible that they would serve as a kind of militia and rapid response force, or perhaps the equivalent of police officers. A warship would probably carry drones and missiles that outperform the dudes in power armor, but you can't have warships everywhere, so the power armor might keep human infantry relevant outside of war zones.
Economical and social impact
Spaceships are expensive and, compared to that, equipping your crew with power armor isn't going to bankrupt anyone. It does, however, set a lower bound on the value of a crew member. That is, purchasing and maintaining the suit has to be less expensive than replacing your crew.
Considering that they don't age and are able to, if needed, think and react at superhuman speeds, it stands to reason that an experienced crew member would be an invaluable resource. They also have practically unlimited time to amass wealth and collect resources. Whether it's due to their own bargaining power or just to protect an investment, I could see the more senior crew constantly upgrading their armor and augmentations as they advance in rank and age, becoming more powerful but also less human in the process.
In this scenario, it will say a lot about your society how they treat young people. Are they expected to spend their first thousand years as cheap, expendable labour? Or are they immediately given the means to contribute and compete in a society of, by a young and broke person's standards, ancient demigods?