How do constellations expand their star fields?

It is not a hostile relationship with other countries in the middle (an important prerequisite)

Diplomatic negotiations, asking the other side to allow civilian ships to pass (not to mention warships, even 99.9% of small countries can't sail).

After the other party accepts it, use the folk immigrant ship to sail to the target planet (if the other party agrees, the scientific ship/engineering ship/immigrant ship can pass through its territory).

Colonize > build stations > outpost > and then you can expand to the edge.

After having a new territory, you can set up a star domain according to the situation and recover the colonial space before expansion.