IGN provided this helpful piece that places Monarch: Legacy of Monsters within the broader Monsterverse continuity.
As a timeline refresher: The Monsterverse Godzilla movie that centered on the catastrophic G-Day event happened in 2014. Season 1 of Monarch: Legacy of Monsters followed one year later in 2015 and ended with a two-year time jump to 2017. That was a result of the semi-successful rescue mission executed by older Shaw, Cate Randa (Anna Sawai), and May Olowe-Hewitt (Kiersey Clemons) into Axis Mundi, the pocket realm between Earth and Hollow Earth, to rescue a stuck-in-time Keiko. Season 2 then unfolded over a breakneck eight weeks in 2017, leaving about 18 months of open storytelling time until the Titan awakenings featured in Godzilla: King of the Monsters.
There’s still a lot of social media debate out there however regarding the appearance of Rodan first in the continuity at the end M:LOM season two. Is it the same Rodan who appears later in Mexico in Godzilla: King of Monsters? Or, are there two distinct Rodan’s?
Since Rodan is a classic Toho Kaiju licensed to Legendary Entertainment, it’s a major commitment towards a third season narrative either way.
I really prefer the work by the team that’s now in charge of the television side. But they received a lot of negativity for K:SI so it seems the television medium is a better fit.