For context: My party is prepping an ambush on some enemies. My character, the Fighter in question, is going to betray an allied NPC and attack them before the ambush goes off.

Do I get my Extra Attack action on the NPC?

Why would they not?  Someone declares that an attack will be made, the DM figures out if anyone is Surprised, (you will have a hard time getting Surprise if you're wearing medium or heavy armor since that gives you Disadvantage ) positions are checked, and then Initiative is rolled.  As long as you're the one who declares the attack, and you win the Initiative, you're perfectly able to get all your attacks in.  Attack twice with the first weapon, if you have a second one, attack with that as your Bonus attack, and if they try to escape, another hit as a Reactions.  Burn your Adrenaline surge for one more attack with the main hand weapon.

If you lose the Initiative, well, they get to fight back.  That will probably spoil the ambush, but you still get all your attacks in.

For surprise the rules say:

"The DM determines who might be surprised. If neither side tries to be stealthy, they automatically notice each other. Otherwise, the DM compares the Dexterity (Stealth) checks of anyone hiding with the passive Wisdom (Perception) score of each creature on the opposing side. Any character or monster that doesn't notice a threat is surprised at the start of the encounter. "

I would rule there is a difference between "noticing" the other and "noticing a threat". I might be wroung I understood from the OP that the party and the NPCs are together and aware of each others presence so have noticed each other but are allied so may not notice a threat. As the fighter is trying to deceive the NPC (and probably the whole party) that he is not a threat I would have him roll deception against the insight of the rest of the party/NPCs. Anyone who sees through the deception notices the threat to the NPC and is not surprised while the others are surprised at the fighter suddenly attacking the NPC they thought was his friend.

Quote from Geann >>

Why would they not?  Someone declares that an attack will be made, the DM figures out if anyone is Surprised, (you will have a hard time getting Surprise if you're wearing medium or heavy armor since that gives you Disadvantage ) positions are checked, and then Initiative is rolled.  As long as you're the one who declares the attack, and you win the Initiative, you're perfectly able to get all your attacks in.  Attack twice with the first weapon, if you have a second one, attack with that as your Bonus attack, and if they try to escape, another hit as a Reactions.  Burn your Adrenaline surge for one more attack with the main hand weapon.

If you lose the Initiative, well, they get to fight back.  That will probably spoil the ambush, but you still get all your attacks in.

What does medium/heavy armor have to do with whether or not an enemy is surprised?

The disadvantage on Stealth checks will usually ruin any attempt to sneak up on an enemy. That's likely not relevant here since based on the scenario the Fighter probably isn't trying to sneak up on the friendly NPC, just catch them off-guard if they don't suspect the betrayal.

Also note that even if you lose initiative, if the target is surprised you'll still get the first strike, though they'll be able to use reactions.

Quote from Geann >>

Burn your Adrenaline surge for one more attack with the main hand weapon.

If you mean the Fighter's Action Surge, this actually grants more than a single extra attack if you have Extra Attack; it's a whole extra action so you can do everything with that that you would do with your normal action, so from 5th level you can make 4 attacks (5 with two-weapon fighting) in a single turn, from 11th you can do 6 (or 7) and from 20 you can do 8 (or 9).

Nothing surprises a former ally quite like four (or five) blows to the back of the head. 😈

Honestly if you stab people "out of the blue" I would not let it be dependent on initiative as it is not "combat" per se. If they're not expecting it and it's pré ambush (unless it's like 5 sec before) you just attack him... You stand behind 'im and just shank im in the back end of story. Honestly doesn't even matter how many attacks you have if he's unaware of your betrayal.

Creates a much better narrative style than rolling initiative to flog down a poor guy who's being betrayed by his allies and it also doesn't bog down gameplay speed.

Playing a Fighter who is a multi-HIts deliverer it will be so OP at lower lvls. The DM should nerf you ASAP if he/she detects such hacks.
It's better performing an attack that could stun the opponent ( using the spell Power word: Stun , or any bludgeoning weapon ), so the enemy gets incapacitated until the next turn. Then, at your next attack, you can make 2 or three attacks again.

Wherever you see problems, I see solutions, babe.

Quote from Dertinus >>

Playing a Fighter who is a multi-HIts deliverer it will be so OP at lower lvls. The DM should nerf you ASAP if he/she detects such hacks.
It's better performing an attack that could stun the opponent ( using the spell Power word: Stun , or any bludgeoning weapon ), so the enemy gets incapacitated until the next turn. Then, at your next attack, you can make 2 or three attacks again.

Wherever you see problems, I see solutions, babe.

 Absolutely none of that is correct aside from the fact that Power Word Stun can be used to stun enemies.

Being able to make multiple attacks is not OP, it's literally the point of having the Extra Attack ability and as that's something that can't be obtained before 5th level it's hardly in need of nerfing.  Nor do bludgeoning weapons stun or incapacitate the target.