Well Nhazul doesn't really have any abilities that would allow him to bypass Bowser's Type 2 Immortality and Regeneration, though he could probably deal with Bowser's 48.73x reaction speed by using his Precognition. Bowser could probably reasonably beat Nhazul in a 1v1, as I don't think his regeneration is enough to bypass balls of magma and energy exploding all over his body while Bowser abuses his massive LS advantage.
Well...Nhazul is a much smarter fighter than Bowser is, and given that he lacks his other equipment besides the star rod the only way to abuse his LS is by ripping Nhazul in half (which he could 100% do, but Bowser would have to catch him first). His precognition is going to help him a lot here (plus the fact that he'd be able to "smell" Bowser's magic), but so is his fear manipulation and the fact that he can double his speed and strength via Red Rush...his type 2 immortality is going to save him from some attacks, but it only revived him after he got all of his skin blasted off, and crushing that bone is going to make it much harder to regenerate from :0
Soul is definitely the better equiped fighter for this battle by having Invulnerability, Plantfields, 10 Duplicates, Flight (Restricted and Non-Restricted) and Hurricane Air Manipulation, Giant Lasers that deconstruct on the Atomic level, Metal Manipulation (Bowser has seemingly Iron spike bands in his limbs that could probably be manipulated), Invisibility, Fear-Inducing Aura, Soul-stealing Scythe, Disco Ball of forced dancing, Martial Arts and regeneration by eating food (Up to High-Low I think?), but at least Godzilla could probably reduce Soul into nothingness with his Quantum level Atomic Breath and Bowser has his 1,608.35x faster lightning : )
Well...multiple characters within the franchise have shown themselves capable of tanking Godzilla's quantum breath (such as the female MUTO, although for a limited time). The notable attacks/techniques section mentions that it's likely used as a last resort attack as well, so it's unlikely that he would fire it immediately nor that he would reduce Soul to nothingness with it. To Godzillas benefit, however, he's one of the few characters in this tournament who are capable of taking multiple of Soul's lasers without dying via sheer size alone (although Soul making himself larger may negate this issue).
His regeneration via food is up to low-mid (albeit with only 1 food) if needed, but yeah most of the foods practically max out at high low :3
Bowser's lightning is only effective within tens of meters, while many of Soul's lasers are going to shoot off hundreds of meters...the invulnerability while moving will help him take a lot of Bowser's attacks, and that's not even mentioning the fact that he's also invisible while running as well :0
But in all seriousness, Bowszilla's best wincon is probably Godzilla using his Explosion Manipulation from his Burning key, assuming it's also on the Quantum level due to it being called an "energy explosion" and Zilla's energy manipulation being attached to his Radiation and Matter Manipulation in the first key. Godzilla would also be aware of Soul's position by using his sense of the atmospheric and tectonic shifts of the Earth, so that would definitely help if Zilla tried to use the standard Atomic Breath from a 4km distance instead.
Well...
"This ability is based on Godzilla releasing excess energy; he cannot maintain this state without suffering a grievous injury.". Godzilla can only use this while he has excess energy, something that he's not going to have in the match...the only thing with radiaton is Soul's radioactive lemonade (something that Godzilla won't know he has) and the energy absorption doesn't look to be the most combat applicable thing (The link shows him absorbing it from some sort of hill?). Godzilla's going to be too busy fighting to absorb energy as he does.
As for the extrasensory perception?
"Godzilla has permanently gained a heightened awareness of the tectonic and atmospheric interactions of the planet as well as the Earth's early geothermal history" and "The narration in Godzilla Dominion states that Godzilla views the world's oceans as "an extension of himself"". I'm a really casual Godzilla fan, and from what I could tell from the movies this doesn't seem to be something that he can use to sense other smaller creatures. Kong (who's comparable in size to Godzilla) couldn't find a girl who was yelling at him at first, and when Kong himself was chained to a ship it took him absolutely going apeshit crazy with yelling and tugging for Godzilla to notice. Noticing characters as small as Soul & Nhazul from super far away via his extrasensory perception alone would require them to either be making loud noises or firing off shots early, which neither of them would do in character >:3