I know it is hard to analyze, but the idea being that it doesn't exclude potency buffs, it just serves as an equalizer in some of the more frustrating aspects of being a caster. Having abundant overflow capacity for Mana means you could reserve a melee combo for movement where it allows, instead of having to stutter step or resort to VerScathe, or if stutter stepping is possible, more room to store more mana to prevent overflow if a raid window is opening up.
Practically speaking, this is a 'neutral' change in terms of potential DPS, but should be a notable uptick in terms of practical DPS - Which is what the Shadowbringers changes largely did for Black Mage, with the exception of Despair and even more enhanced Enochian, which is where a fair amount of its damage potential increase came from.
Manafication is largely a change to let Red Mage -get it on- like everyone else does at the start, however with this mind it would work better as a +80/80 in the 160 gauge state.
And Embolden, aside from being a straight buff, also allows the Red Mage to more readily capitalize on its own windows with more frequent use and a duration that matches (10.5 total seconds for a melee combo, though the damage is done by 8.0, so it all gets the 10% increase).
I think this serves to not only close to gap but make playing a Red Mage 'feel' better. From a hard RDPS standpoint, the Embolden changes alone should increase the "RDPS given" value by nearly double by virtue of no more decay and affecting casters, while having more individual control over Red Mage's outgoing damage and pacing should make reaching the maximum less RNG dependent. Affecting casters also means you don't have this weird case where the only two caster set up you would want auto excludes red mages.
Regarding Summoner, I've got too much "I want to change everything about it" to offer a bandaid fix, but moving Egi Assaults to the GCD and greatly increasing their potency would be the path I'd take, as well as completely turning pets into visuals and sourcing their attacks from the Summoner (AKA - no more ghosting attacks)