GRNs push into Magellan, Cortez and California is because lore-wise the Navy isn't fully deployed like it is now. Liberty still has a plentiful fleet at home ready to combat any threats that arise. Rheinland has to act soon, Munich is almost completely gone and the Sigma war has stalemated now that it's involved Kusari on GMGs side. Liberty's forces are sufficient for a multi-front scenario, backed up by the plentiful forces of Whitefield, Fairmont, Rio Grande, Missouri, Mississippi, alongside their respective taskforces.
Combined with Libertys wide industrial capability, Liberty has the most sustainability for a multi-front scenario. Liberty's just now getting fully set in the war, and has sufficient forces to brute force their way through Magellan and Cortez with acceptable losses. If a second war between Liberty and Rheinland breaks out, Liberty has sufficient forces to hold the line in Hudson. It would be a gamble for Rheinland, as the new Kusari Empire may see it as an opportunity and turn the Sigma War into more than just a border skirmish and launch a full attack on Rheinland. Rheinland would then be pressed into a multi-front war alongside any issues that arise from the south.
In this scenario, Rheinland wouldn't be able to divide forces very efficiently to counter a full invasion from a Kusari combined fleet while keeping Liberty at bay aswell. One front would fold with time, they'd have to choose to stand their ground against Libertys war machine and declare the Sigma's a sufficient loss and face invasion in Stuttgart, or fight Kusari and GMG in all-out war and hope they secure enough ground to replace the losses they'll take in a Libertonian push.
Gallia's current war situation puts them in a bad position to issue demands from the Kusari Empire, they cannot risk opening yet another front from Kusari skirmish forces. The bulk of Gallia's forces are too entrenched in London to pull back now, and the majority of their home fleet is tied down fighting the Council with varying success. They cannot risk another organized military entering the fray against them, as a Kusari skirmish force would choke out Gallic supply lines with raiding forces, and Gallia has precious few assets left to make an assertive action against Kusari.
Edit: Also, Rheinlands already in the process of replacing Ageira with EFL anyway, a war would only speed things up.