Lots of frame challenges are possible. But I'll answer straight instead. I'll also assume that the magic stops any combustive propellants, not just gunpowder, so you can't just use rockets like the Gyrojet.
This is not to be confused with electro-thermal-chemical, which combine ET with high-power propellant. Electrothermal weapons store energy in a supercapacitor and discharge it to quickly vaporize a neutral, non-combusting propellant.
This is a modern high-tech option that will be most similar to existing guns in performance. You do need to charge it, like a phone, but the solid for heating can be packaged inside a cartridge, like in a modern handgun.
Supercapacitors store up to 100 Wh/kg and release energy at 15 kW/kg. To overcome the second limitation, you'd either add a charge capacitor or a membrane in each cartridge, which breaks at firing pressure. 15 kW gives you 10 shots per second at 750 joules/shot and 50% efficiency, so even an automatic is doable, with a 1 kg capacitor good for 30-50 shots.
Both options bring the drawback that the gun will take a bit of time to fire. For a pistol-sized weapon with a smaller capacitor, it will take about 0.2-0.3 seconds from trigger pull to a full power shot, if a bursting membrane is used. If a charge capacitor is used, the gun can fire instantly, but it will leak energy while charged.
Still, even with these limitations, it's practical, powerful, and possible with modern technology. Electrothermal tech is being considered for next-generation tank guns, as it can pack more energy into a shot than gun propellants.
Supercapacitors and high-power electronics are expensive, though. I've done some research a few years back, and a reliable personal weapon would cost high four figures. It's still not an unseen price for high-end firearms. Plus, in a world where they're actually necessary, your electric car will probably have a charging rack for your e-guns.
Already covered in other answers, this is the go to gun for less-lethal self-defense. Unlike mace, it doesn't rely solely on pain. Unless you need to pierce armor or match the magic's range, in which case you go to...
Citizens who can't afford electro-thermal guns, will have to settle for pneumatic or spring-powered weapons. Spring power is limited and difficult to reload. Compressed air is much bulkier than gunpowder, but you can fire off multiple shots even in an emergency.
The most lethal and reasonably long-range option, if we exclude guns, is crossbow bolts.
This is one such airbow. It does look like a gun... it does work like a gun. They are used for hunting. A standard bolt at 450 fps has similar 250-300J energy to a small handgun, but can be considerably deadlier with the right tip.
Or can pierce armor if needed. You can guess who fields a subsonic armor-piercing rifle. It's automatic and a crossbow isn't, however.
Let's not forget high-tech airguns. A .457 hunting airgun delivers 600 joules of energy - more than a .45 ACP pistol bullet. In comparison, common BB guns and airsoft guns produce 1-2 joules. Anything above 100 joules is firmly in the lethal category, and a 600 J weapon can be used for big game.
The secret to these airguns is pre-charged high-pressure air, storing almost firearm-like pressure in a steel or carbon fiber tank.
These figures are obtained at 3,000 psi. Fill tanks are loaded to 4,500 psi and storage tanks to 6,000 psi. This allows for easy top-down filling through pressure regulators.
If someone is willing to use a boost compressor rather than a regulator to refill their gun, or just get a factory-filled 6 ksi (ksi=1,000 psi) tank, they can double their power, reaching rifle levels. Or, better, apply that to pneumatic crossbows - I find them cooler for a magic-enabled setting.
One reason airguns don't go to 6,000 psi (or even 16,000 that's been used industrially) is noise. Noise depends on muzzle pressure, and a 3,000 psi airgun doesn't scare prey as far away as a 10,000 psi shotgun. Similar pressure will mean similar noise. But if guns don't always work, you'll see a competition for power and pressure in airguns, and it won't stop at 6 ksi.
So... volts or bars?
The common limitation of air-powered weapons is that they remain subsonic. Some can reach Mach 0.9, but that's it; air only expands at the speed of sound, and it gets cold in an airgun. Bolts can still penetrate armor at subsonic velocity, due to their high sectional density. Modern tank rounds are basically supersized uranium bolts.
Electrothermal guns have no such limitations. They heat up the gas, and hot gas has a higher speed of sound, so they can fire supersonic, rifle-like bullets. Even out of a short barrel.
Air also has a limited capacity. Hunting airguns only store enough air for 4-8 shots, with slow reloading as you have to open and close the valves. Electrics are going to start at 30, and battery swaps are as easy as a magazine.
Why not both?
It's also possible to combine the technologies - superheating the compressed gas with an electric discharge, to push the round to high supersonic velocities not possible for pneumatics. A pure electric will be simpler, but with a hybrid, you can have the reliability of pneumatics and the power of electrics if charged.
The cost and regular maintenance required for electrics will be worth the capacity and firepower for combat professionals, since they carry a Christmas tree's worth of battery-powered gadgets as it is. An air cylinder, on the other hand, can store its pressure for decades without decay.
You will probably see electrothermal weapons in police and military service, and high-pressure pneumatics plus the good old TASER used by civilians. Hybrid weapons are likely to be available as high-end civilian/sporting options.