from what i can tell ships only gain experience via battles.

maybe they should add a tiny thing like:

1-gaining 1-3% exp of a lvl per week(so a scout you created on day 1, will have gain a lvl at turn 33-100), and in battles you gain much more.

or

2- survey ships gain a tiny bit of exp from going around and ships gain tiny bit of exp based on exploring (amount of distance covered and so on).