I don't think they need to make magic non-existent. The Colleges certainly didn't exist, but one of the big strengths of Three Emperors as a setting/era is how Game of Thrones'y it is in terms of power dynamics between and also within the different factions, and there's certainly room in that context for a ruler who's powerful enough relative to the Cult that supports them to establish something organised but smaller-scale. The Wizard's Mansions in Mordheim hint that magic may have been tolerated there at some point, and the Great Library there had a huge collection of arcane lore. There's the old 1E RPG fluff about a school of magic in Middenheim that existed prior to and independent from the Colleges, and while they retconned that into being just a "satellite school" of the proper Colleges in modern background, there's nothing stopping them partially re-retconning that into being a school that existed prior which was then legitimised as a satellite school by Magnus.
Without the self-policing organisation of the Colleges and given the general state of turmoil of the period, there's also more scope for "evil vizier" type figures - warlocks and witches and necromancers who inveigle their way into the good graces of some noble or ludicrously wealthy mercenary leader.
No I don't think magic has to be non-existent, but it does need to be different, both in the fiction and mechanically. And, should we end up with subfactions, there should be incompatibilities of course - your noble can hire a shonky warlock, but not at the same time he petitions the Church of Sigmar for aid; your Middenlander general can call upon a sorcerer from the school in Middenheim, but not if he expects to be accompanied by Ulrican templars.
As for gunpowder, it seems as if the Empire followed broadly the same path that we did IRL with two exceptions - Dwarf-made anachronisms available to the very wealthy, and the warped timescale. It seems like most of the Three Emperors era would have been covered just by the evolution of matchlock firearms, with wheel- and snaplock mechanisms being developed between Magnus and the "present day", and Engineers just starting to experiment with flintlock style mechanisms around the time of Karl Franz. That makes some sense in the context of understanding that war tends to advance the implementation and refinement of new technology, but will stunt theoretical research if it goes on for too long so starving the society of new technologies to implement or refine. 800 years of internecine war punctuated by Waaagh!s and Northmen rampages capped by the Great War would leave little resources for "high concept" research, and there would have been a period of comparative peace following reunification.
How much of an impact that should have on the rules or availability of firearms would depend where in that 800 years TOW ends up being set. Early on they should be a rare and awkward curiosity, by the Mordheim-to-Magnus period merely expensive and cumbersome.
Honestly I'm less concerned with when it's set than whether they're going to "modernise" the setting in a performative way.