For the Stunned Pilot Critical effect, we had a situation in game that we could not find the answer to.

The card speaks to taking a damage whenever your ship overlaps an obstacle after performing a maneuver.

What happened in our game was after a ship with no faceup damage cards did its maneuver, it overlapped an asteroid and rolled for damage. They got a critical. The card that was drawn was the stunned pilot card. Since the ship had just taken a maneuver, does it take a damage immediately upon drawing the card since it technically just did a maneuver and ended up on the asteroid or does this not take effect until the NEXT maneuver?

Next maneuever. It's already completed its move before the card was drawn so the trigger window has already passed.

Also just FYI, that particular crit only triggers if your final position overlaps an obstacle, not if the template does. Your ship is only considered to have overlapped an obstacle if it lands on it. The rules for the usual interactions with obstacles specifically say "if the final position of the ship or the movement template" overlap the obstacle you roll etc. The crit just says ship. So you may fly through an obstacle with that crit and not trigger it as long as you end in a safe location.

There's a slightly contradictory ruling for Advanced SLAM. When they wrote the card they just said "you overlap" rather than "ship or template". They wanted it to use the same rules as a standard maneuver but messed up the wording and then rather than errata it they just gave an FAQ ruling to say that's how it works despite not being what the card says. I only mention it in casr someone tries to use that as a precedent