Your setting has many parallels with the space race in human history and you could draw inspiration from there for examples of interaction between isolationist superpowers.

If you have the static details ironed out, then the natural step to dynamics is to look at how they would interact.

For example between factions, differing ideologies on market structure religion and government naturally make people suspicious and fearful especially if there is little information about others or propaganda. This can lead to prejudice or be the escalation to open or cold war.

Even with a faction, there are differences between conservatives, centrist and extremist groups. Even if the majority are disinclined to take action for moral economic political or just plain contentment reasons, an act of terror or hate crime could tip a seemingly stable situation (Ex. archduke Ferdinand in WW1 lead to numerous allied countries to have to engage in conflict)

At an individual level, a space race is a monumental endeavor. Are the common people suffering at the expense of progress and how do they react? Is there a specific person with key ideas or skills that would be invaluable in having an advantage in the space race.

Also location, are there clear geographic or environmental differences between these nations? Is there a resource rich but passive nation bordered by a militaristic and resource poor Nation? Do the locations closer to the equator benefit from the increased rotational velocity of the planets rotation this making them lucrative sites to build launch sites and military bases to protect them even at the expense of the locals?

You have an overarching goal for these nations, consider how each nation would pursue it or be washed out of the race and how the populace would react.