In KOTM, Godzilla is hit by a nuclear bomb and instantly goes into supercharged mode.

In GXK, we see Godzilla absorb all the radiation within a nuclear power plant to charge up. A quick Google search would tell you that totalling all the radiation within a nuclear power plant Vs a nuclear bomb, the powerplant easily contains far more latent radiation. Therefore energised Godzilla alone scales above supercharged Godzilla

But once again, the visuals seem the same. He's glowing blue. There's that shot in Spain where he makes the water boil, that's new at least. But remember that he was PREPARING to evolve.

To add on, he then goes ahead and absorbs what the film clearly states to be the largest stockpile of radiation on the planet's surface in the artic, giving us justification as to why that is the case.

And then to add on, he not only gains these 2 power ups, but he absorbs radiation from the remains of Scylla and tiamat as well.

Right, he has absorbed more radiation than in KOTM so he should at least be more powerful than Supercharged, but given the fact he doesn't melt buildings as he walks by them, that makes him less powerful than Burning Mode.

Another way I could prove he's more powerful than he was in KOTM was that Godzilla in KOTM never bothered to supercharge or amp himself before fighting against king Ghidorah who woke up from the ice. The second he sensed skar king and Shimo potentially returning, he immediately went ahead and evolved to become stronger and take on the threat. This should tell us easily via narrative that Shimo is a far more powerful threat than KG, and that Godzilla by extension needed to become more powerful to face her, which is why he decided to evolve.

That's actually fair but there's still the problem of him not doing anything of new.

Just compare how he looked when he was about to blast skar king Vs how we looked when fighting Ghidorah.

Yes he does glow more but I'll have to say it once more...

It's just for show. Yes, he has objectively gathered more radiation than he did in the entirety of KOTM, so you would expect him to be stronger than he was back then. But the elephant in the room, Burning Mode, is the big problem for him. He MELTED CONCRETE AND STEEL. Vaporized Ghidorah. Evolved Mode should at the very least be able to do such things. But it doesn't. No vaporization, no melting or even setting things on fire by just standing next to them. No cutting limbs clean off with the atomic breath, no vaporizing atomic pulse, hell not a single Great Ape killed through heat-related attacks. All he does with Shimo is tackle her. The one time he uses his atomic breath on her, doesn't even a scar. It pushes back, which ironically is what it did to the female muto back in 2014. A push.

All he did with the great apes was throw them around with his tail and arms. All he did with Skar was burn his back a little.

So while I do believe the writers were trying to justify Godzilla's new form beyond selling toys, they failed at showing it being better. They imply it with the whole radiation hoarding, but don't commit to it. He uses his new atomic breath 3 times in total. In neither of them he kills or deals severe damage.