Relatively new to the game and apologies if this is already answered somewhere obvious:

If a ship would flee the battlefield if it fully executed its maneuver, but is unable to execute the full maneuver because it bumps another ship, is it destroyed for fleeing, or does it stay on the table where it bumps?

We played as the ship staying in play with the logic that if it can't complete the maneuver, it can't flee the battlefield.

Thanks in advance!

You only "flee the battlefield" if your ship base is off the mat at the end of your move. Bumping stopped your move where you are so if you are NOT hanging off the board you have not fled. Reverse is also true though, if a bump causes you to stop short of your intended move and you have part of your base now hanging off the mat you HAVE fled and must be removed from the game.

Yup, if you do a 3hard and the template goes off the board, but your ship isnt, you didnt go off the board. Its all in the final placement. Same goes for unable to complete a maneuver, if your final position is not off the board you are still here. Though i cant think of any way to escape such a situation next round lol

Its really difficult to intentionally bump someone to go off but its easiest against large ships, since almost any bank near the edge risks poking the borders.

It's being mentioned but final ship placement is all that matters.