Does anyone know the details on how crew affects ship stats?

Pilots are the primary contributor to your ship's stats. Everything about them matters - gear, stars, level, mods (to a minor extent), and even ability levels. However, regular stat differences don't matter - only these 5 things listed here. Some aspects are more beneficial than others, and the higher you go in any one area the bigger the difference (going from 6 to 7 stars has roughly the same impact as going from 2 to 6 stars).

Something of note that many seem to miss: Mods do NOT affect ships the same way they affect characters. Only the tier and level of the mod matters; primaries, secondaries, and set bonuses do not.

Watch out: crew power != crew rating. Crew rating, which is what the game uses to calculate your stats, is hidden and based off the 5 character aspects. Crew power is essentially a rough reverse-engineer after calculating what the ship’s stats would be without the pilot. It’s weird, somewhat convoluted, but it is what it is. Don’t be misled.