So the question basically is what did godzilla want in Godzilla vs Kong?

He attacks because Apex is building a Mechagodzilla, a giant robot that can go toe-to-toe with Godzilla and other Titans. One of Mechagodzilla's eyes is in the lab, and it's putting out a signal that Godzilla doesn't like.

Godzilla came back and beat Kong - which makes sense given Kong's wounds and Godzilla's nigh-invincibility, as well as his ability to absorb radiation to recharge himself - but rather than kill him like he did the MUTOs and Ghidorah, Godzilla initially left Kong to succumb to his wounds, then later forced Kong to then later forced Kong to kill him.

conclusion: It will not kill Kong in a single hit, and Kong won't allow subsequent hits, in order for the movie's plot to progress. Anthony Perez, True Godzilla fan here to help. No he will get severely burned and if Godzilla continues to use his Atomic breath its game over for Kong.

Scale up that strength to Godzilla's size, and that tail becomes a lethal weapon – which he has used before. However, Kong is more comfortable on land, faster and more agile, can use his strong legs to jump, and possesses much stronger arms than Godzilla – Kong probably packs a walloping punch