wrong - that would be 7 attacks (2 from extra attack, 2 from action surge, 1 from haste, 2 from unleash incarnation since you take 2 attack actions).
No. Casting Haste takes one action.
Action: cast Haste (0 attacks)
Action Surge: Attack action - extra attack (2 attacks), Unleash Incarnation (1 attack)
Haste: Attack action (1 attack)
That is 4 attacks total. It would be 5 (not 7) but the Haste spell has a disclaimer in it that when you take the attack action as your extra action you get "one weapon attack only"
If you have a bonus action attack it would also be 5, but then you are doing less damage with all your attacks because you are using a weaker weapon. With PAM on the other 4 attacks you are giving up 10 damage (with a pole arm) because your base damage is lower and your strength is lower (and have a lower chance to hit). If you used 2 weapon fighting you would be giving up 16 damage on your other 4 attacks.
for however many more turns as you have unleash incarnation it'd be 4 attacks, and then it'd be 3 until haste ends. that goes up to 8, 5, and 4 attacks respectively with PAM, but that attack does different damage.
And that is irrelevant because you have no divine smite slots left after halfway through the 2nd turn (assuming all of them hit)
assuming those all hit and you have a halberd or glaive and 20 strength, you're looking at 81 damage from just the halberd and PAM, and 94 damage from smite, for a total of 175 damage.
But with average rolls or point buy you would not have a 20 strength and PAM with only 2 ASIs.
Average damage if you actually did get
7 attacks against an AC17 foe with 18 strength and PAM using your best available slot is
94.2 DPR. That includes crits.
That is with 7 attacks. With the 5 attacks you actually get when casting Haste and with PAM it would be 75.2 damage on average.
If you don't like those numbers, give me the ones you want to use, but regardless of what is used it will be nowhere near 175 damage in a single turn at 12th level.
crits could absolutely get you to 300+, though you'd need to get pretty lucky.
Even with 7 attacks the chance for 300 or more damage is less than 1 in 10 million. It is actually too small for the numerical method used by the program I use to calculate averages and percentages.
5th level smites aren't a thing. the damage caps out at 4th level.
That is not how I read the description of Divine Smite:
"The extra damage is 2d8 for a 1st-level spell slot, plus 1d8 for each spell level higher than 1st, to a maximum of 5d8."
The way I read that is a maximum of 5d8 extra (above the initial 2d8) or in other words it caps out at a 6th level slot. Regardless if a 5th level slot only 5d8 instead of 6d8 then that means it even fares less well as compared to a spell.