There is also a possibility that the Godzilla KotM manga will continue the events of the Godzilla vs. Mothra manga (Kodansha) instead of the movie, don't you think?
I think Koopa would be a better person to answer this, but on the latter point, I know the manga makes reference to the movies. Namely, Oniyama views footage of Godzilla and Minilla being frozen at the end of Son of Godzilla (represented by a screenshot from the movie). There are also things like Baragon being mentioned to have fought Frankenstein, and certain monsters like King Ghidorah and Mechagodzilla being established as one of multiple individuals which have appeared before.
While there isn't a definitive diagram stating that KOTM is canon to vs. Mothra, the penultimate chapter opens with Oniyama finding Battra's frozen body deep in the ocean, presumably from where Godzilla killed him in the film. As for whether it's canon with that film's Kodansha adaptation, I'd need to read the latter to be sure. Hisashi Yasui wrote the stories for both, so it's definitely possible, though given the vastly-expanded universe of GKOTM - one in which at least some of the Showa era events took place, given the presence of King Ghidorah III, Mechagodzilla III and Mechani-Kong II, there is a chance that the GvM adaptation is more strict in how it approached translating the original story into written media.
I would really appreciate it if you could check the Godzilla vs Mothra Kodansha manga, as it may be that the GKotM manga is only canonical to the manga version of Mothra's movie. Thanks in advance!
There is one big piece of evidence against KOTM being a sequel to Yasui's adaptation of GvM - our page on the adaptation states that Godzilla kills Battra by punching through his head, but in the KOTM manga, when Oniyama happens upon Battra's frozen body, his head is fully intact.
In the Movie, Battra was dropped in the open ocean, It wasn’t specifically in the North Sea or at the north pole. If not, it looks like the manga connects specifically to Yasui's written adaptation.