Anyway, I'm under the assumption that Gram will be unrestricted.
There are a couple notable factors that swing this match around a bit, firstly Sigurd is coming with a slight AP disadvantage this time around as Cole scales way above 340 megatons while Sigurd scales around 500megatons after revisions.
Secondly, unlike the last match Speed is Equalized, which means Cole goes from being nearly screwed in CQC under the decent chance he can use his speed to dodge, to being utterly screwed because he no longer has that.
This Cole has actual flight, which allows him to play the range game flawlessly against Sigurd who's only ranged attack is the 6C Gram, which one shots Cole due to the AP difference, however, due to the massive distance, Speed Equalization+Precision to amp Cole's speed (Yes I am aware of Mana Burst)
On top of this Sigurd, of course, has the soul cutting Death Rune, meaning one hit will give him the win.
Basically, Sigurd needs to cover the massive difference in distance with either Gram or straight up charging him in CQC.
Now there are a couple ways that Sigurd can get around this, Runes for defensive shielding against the majority of Cole's projectiles although I'm not sure of how long they can stay up nor how high their AP is, I will highball it and say that they can stay up as long as he wants them too and have the AP to take minor hits. Cole can bypass this by using the RFI and it's constant source of energy to bombard the shit of Sigurd and using his flight to dodge Gram, both have enough stamina to fight for hours without tiring so stamina is no issue for both.
However, like said, Gram will not be able to reach Cole with it being non-homing and all. Due to this Sigurd will have to eventually stop turtling, and this is where Cole can really do some damage, as Cole no longer has the shielding to worry about.
Here's how I see it going.
Sigurd and Cole may not instantly see each other but they still know generally where their direction is, Cole immediately takes flight, as is extremely in character for him, he loves range spamming and spamming pseudo flight at any given turn and when he does get true flight he uses it instantly.
Sigurd immediately recognizes where Cole is and starts Gram Spamming and using Runes, Cole counters by merely sidestepping, or Side Flying in this case. Speed Equalization and massive distance means Gram won't hit him, runes means Cole can't do much to Sigurd.
Sigurd either eventually loses in the long run due to Cole's far superior range game and versatility with projectiles, or Sigurd attempts to close the distance, only to realize Cole hits him and hits incredibly hard, also Precision makes Sigurd look extremely slow by comparison which will allow Cole to get some good hits with his projectiles.
Now to counter a point that was made on previous Sigurd vs Cole threads, Magic Resistance, this is a moot point here, and I'm going to repost reasons why from previous threads.
"The problem then arises, if his lightning has Mystery and is thus magical, MR negs it to hell and back unless there is some explanation in verse that would prevent his lightning schtick from being verse equaled to thaumaturgy."
"Cole's lightning is, rather explicitly, non-magical. There's no magic to it, just Psuedoscience. But, under Nasuverse rules, Cole's abilities would have an absurd amount of mystery because of his unique nature, and the mystery of how he generates and controls it.
I don't think Sigurd's MR would block it. Mainly because, well, it isn't magic. It's just really strong electricity."
Verse Equalization is far too loose to go so far as to make something that's pretty explicitly Science and Biology in verse and make it magic, when it has about as much magic as reinforced Fists from Soichiro for example. (It's also just too loose in general, RIP Bleach Matches)
Cole takes this 9/10 times, only reason this isn't a stomp is due to Sigurd needing one hit, and I repeat, one hit with literally anything to win, but Cole simply crushes him in range combat due to the combination of true flight+Massive amounts of projectiles including homing stuff+Prescision to amp his speed. AP due to his scaling chain etc.