On Last Stand or Supply Deficit, you get a weird "boss" type character, and I'm unsure of one, small, but EXTREMELY crucial detail.

Are they activating without exhausting their deployment card each time they take a turn, or are they never activating, or are they considered active all the time and basically follow all normal rules but get two extra actions which if you are effective with the character anyway are just going to be moves?

Of all the three, the sentence which accompanies them is "Instead of activating as normal" which out of the three is definitely most indicative of the middle possibility, and it fits the most thematically with the concept of a boss fight, where the "boss" is often getting 4-8 attacks (in the case of RGC and Vader), an equal optimal attack economy as the heroes. The latter seems to be the most non-thematic idea of the three, and I think giving additional health equal to the threat or w/e would be better than two extra useless actions, they'll just have to spend them on movement which just means the bosses are faster than usual? So he'll be more annoying and run away to run the clock down rather than stay and try to grind the heroes down?

What is the official ruling on how Bosses are handled in missions like Supply Deficit and the two finale missions?

The "boss" is activating as specified in the mission rules. Instead of activating normally the "boss" is still activating, but does not receive the normal 2 actions per activation.

For most if not all missions like this, the boss figure activates after each hero's activation (or each rebel group's activation depending on the wording), receives 1 action during each activation (instead of the regular 2), and may have a special action specified in the mission rule to spend that one action on in addition to their regular actions.

Reference: https://www.boardgamegeek.com/article/19900313#19900313

So, because each action is a separate activation, for example every one of the actions the boss takes can contain one or more attacks.

Thank you, that is literally exactly what I wanted to hear