They might not have screenshots, but I do.
- never tried to kill Knuckles, let’s him flee multiple times, and immediately befriends him after he learns Eggman tricked him
Sonic briefly knocks Knuckles out cold before Knuckles runs off to confront Eggman. Sonic follows, presumably to continue the fight, and then Eggman electrocutes Knuckles.
spared Merlina even though she almost killed him
Sonic charged at Merlina first, unprovoked, without knowing she'd put up a barrier, and did so twice, seemingly with intent to kill or incapacitate.
never tried to kill Nack and continuously let him run away
Gamma outright attacked Sonic, yet when Amy told him Gamma was good he immediately trusted her and left Gamma alone
That's... a really weird argument to make considering Sonic and Gamma started fighting on Eggman's orders for Gamma to shoot Sonic "full of holes."
Not to mention how Sonic charged toward Gamma, again, seemingly with the intent to kill, until Amy stepped in.
- continuously let’s Metal Sonic run away or at least live, even when Metal Sonic is half broken and could easily be destroyed Sonic’s just like “welp, see you next time Metal”
Uh... Metal Sonic crashes into a wall in Sonic CD, and Sonic 4: Episode Metal implies that he had been left there to rot for "a long time," so...
- sees an Eggman robot (Omega) with Shadow and Rouge and is immediately like “that guys cool”
...Where are you getting that from? Sonic has never said anything about Omega, period, let alone in Heroes.
Also, does the Team Sonic vs. Team Dark fight count for nothing when they literally try to push each member of the other's team into the abyss?
Like... Sonic isn't the Punisher; he's capable of being discerning - otherwise, he'd have just left Emerl washed up on the beach when he assumed Emerl was just another discarded Eggman robot.
You're being disingenuous by thinking we're saying Sonic should be all "die die murder kill" towards everyone.
spares all the knights of the round table who were trying to kill him, even stops one from ending themself and saves another from falling into lava,
Sonic unrepentantly slays the evil King Arthur in the same game, but you're choosing to omit that part.
- continuously let’s Eggman run away even when Sonic has the perfect opportunity to kill or at least capture Eggman (SA2, Heroes, Shadow 05, Battle, Riders, Riders Zero Gravity, Free Riders, Frontiers, Dream Team, etc).
SA2 = You're being a bit bad-faith here. Sonic had other things on his mind at the time, as had Eggman. You could apply this argument to Eggman too and be like "well why didn't Eggman just cap Sonic in the face when he returned to the ARK? :v"
Heroes = Eggman got chased away by the Chaotix.
ShTH = Again, Knuckles chased Eggman away.
Riders = Eggman passed out after seeing what the treasure actually was.
Battle = ...Huh? You mean the game where Eggman gets electrocuted and Sonic not only leaves him there, but laughs about it?
In Unleashed he even saves Eggman, because he could easily have tried throwing Eggman into the lava but instead threw him out of the hole and to safety
You... you think Werehog was sparing Eggman... in that scene where Sonic tore the Dragoon to shreds as Eggman pleaded "Stay back" and "No, don't"? You think that was Werehog showing mercy?
Eggman says several times that the "controls won't respond" after Sonic delivers a hit. Sonic is systematically dismantling the very armor protecting Eggman as they plummet towards the Earth's core.
What do you think is happening in this scene? No shade, I am genuinely curious. Because I don't think "throwing Eggman to safety" is quite the phrase I'd use to describe it.
only ever kills or eternally captures beings who ruthlessly control or want to destroy the world/universe/etc and when killing is the ONLY option.
Why do people always tack on "Sonic only kills when he has no other options" as if it matters? Dead is dead. Either Sonic kills or he doesn't.
- is repeatedly described/mentioned as the guy who believes in freedom and justice,
In the comics. In the games, he describes himself as "just a guy that loves adventure." The comics do not take precedence over the games in this regard.
outright telling us that he’s always given people the freedom of choice unless they impeded/endanger/hurt others.
Dude, you just got gone admitting that Sonic does sometimes imprison enemies out of necessity; that's not "always giving people the freedom of choice."
This isn't that difficult. Sonic is selfishly fond of his own freedom, but he's not going to abide by the platonic ideal of freedom like it's an iron-clad rule he must follow.