Aoyama's navel laser, which many believe to be simply nothing but a laser, is explicitly stated to be a beam of light multiple times within the story, so many times in fact that it's impossible to ignore that it IS a beam of light, and saying anything otherwise, when the story explicitly calls it a beam of light multiple times within the story, would be downplaying and ignoring canonicity.
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13 states that she can "absorb light" during the fight between Aoyama, Ochaco, and 13 themself, as she's sucking up his navel-laser. There's no reason to assume that she'd be talking about anything else, when she's quite literally sucking up his navel laser, as stated in the panel. But this, however, isn't even close to being the only time its stated to be light.
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Invisible Girl states that she can now "yank light and warp it" referring to his navel laser, which she then proceeds to do. This is referring EXPLICITLY to his navel laser, and this isn't the only time that it's AGAIN stated to be light.
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Invisible Girl states that her body allows her to "refract" light after being hit by Aoyama's navel laser. (This ISN'T a reaction feat for Invisible Girl, as the only reason why she could do it, is simply because of her physiology. I do not believe that she is FTL in reaction speed) This yet again proves that Aoyama's navel laser is a beam of light.
Now that we have established that Aoyama's navel laser IS light, we can now get into scaling.
Aoyama's navel laser fires in a straight line, and it's easy to say that anyone who dodges the beam, is simply aim-dodging. You can make that case for Mina during the Sports Festival, who easily dodges his attacks and takes him out of the Sports Festival. However, Mina should scale more to Relativistic, rather than actual FTL.
She was easily dodging the attacks, but the beams were clearly moving faster than her, but Mina was just fast enough to get out of the way, and she wasn't exactly moving faster than Aoyama's beam of light. Mina around this time isn't shown to be that much faster than anyone else, besides characters like Bakugo, as Deku still didn't have control over his quirk at this time, and didn't fellow Full Cowling.
Anyone that scales above Mina should be bare-minimum relativistic, and this is pretty consistent.
You can attempt to argue that Aoyama's navel laser isn't moving at the speed of light, but light almost always travels at the speed of light if you apply physics, and it should be the same here. It's never proven that it's not moving at the speed of light, and we know that light always travels at the speed of light.
This proves that Aoyama's navel laser is not ONLY light, but it travels AT the speed of light.
There isn't an argument to be made about how Deku massively outscales Mina during the Sports Festival, as he trains and gets a better understanding of his quirk, unlocking Full Cowling, Shoot Style, etc, becoming stronger and faster as the series goes on. Anything below Relativistic in base would be a massive disservice, considering even Mina during the Sports Festival can be scaled to Relativistic.
At the bare-minimum Deku is Light-Speed, and at a perfect middle ground, is FTL.
Mirio, while not paying much attention to Aoyama, is also able to react to his laser while his back is turned against Aoyama, proving that he's much faster than his navel laser.
Remember that Permeation IS NOT something that turns on by itself, and Mirio has to active it himself in order for it to work, meaning Mirio did in fact react to their attacks, and phased right through them before they hit him, putting him faster than Aoyama's navel laser.
You can attempt to argue that Sero's tape is moving just as "Fast" as his navel laser, and thus it can't possibly be moving at the speed of light, but Aoyama's laser is CLEARLY moving faster, as it almost reaches Deku, which he dodges right before it hits him, before Sero's tape can reach the laser, or Deku.
Which, is exactly what causes the damage that he was trying to avoid, in the first place. Deku clearly dodges the beam of light coming straight for him, before it hits him, and before Sero's tape reaches either. You can slow the video down and the navel laser is clearly moving faster, and reaches its destination before the tape does.
Meaning, its moving faster than Sero's tape is, though it isn't too far behind. This isn't too much of an outlier considering he's able to tag Todoroki, who, albeit, wasn't exactly trying to fight back until he unleashes a huge ice-glacier upon him before he's able to be knocked out of the ring.
All For One is barely able to guard himself against the attack from Aoyama, and receives damage from his attack.
(Can't upload the panel or find the manga chapter, but Aoyama attacks AFO with his navel laser, which All For One I believe is barely able to block, his arm is smoking and he's received damage from the attack, and says something. You can argue that he did in fact block, this however I can't find so you can not take it at face value, or you can, either way it's fine, everything else though I have evidence for)
Deku is a casual bullet-timer who has been proven time and time again that he's multiple times faster than any bullet, easily dodges Lady Nagant's sniper bullets, and dodges automatic gunfire point-blank. You can attempt to argue that there should be no need, however Deku ISN'T bullet-proof, and would need to actively dodge the bullets, as he's not bullet-proof, and if he IS hit, it could be fatal.
(And, at an earlier point in the series is capable of dodging lightning in one of the movies, which I BELIEVE to be canon, and he does this while weakened. Deku after the Big 3 Introduction is still FTL or Relativistic+ at the bare minimum, as he casually avoids Aoyama's navel laser, which is traveling straight for him, which Deku wouldn't have known that Mirio would phase through, and couldn't have expected him to do so, when his back is completely turned away from his classmates)
There are many more scans of Aoyama using his light as a light-source and brightening up areas, etc, using it as essentially light which his navel laser clearly is stated to be. There's no evidence to prove that it's not moving faster than the speed of light, it's almost impossible to prove that it isn't, it even moves in a straight line and acts similar to how light does, and is verbatim stated multiple times to BE light.
All in all, the top tiers of the MHA verse calc around FTL in terms of reaction speed, travel speed is iffy, it's hard to place how fast exactly they move in terms of travel speed, but in reaction speed, they are certainly FTL, as they are much faster than Aoyama's navel laser pretty casually)
All in all Deku, Shiggy, AFO, are all FTL in reaction speed, at a lowball they're Relativistic+ to Light-Speed, but that's with some downplay, as they are pretty consistently faster than Aoyama's navel laser, which Deku before the War Arc shows that he can dodge it, when he isn't expecting it, and at the perfect time before it strikes with the ground, creating a smoke cloud/crater.
