The principle problem with your idea is one of focus, I'd say.
The smallest spot size your microwave weapon could be focussed on is limited by diffraction. The size of that spot is defined as
$$R_T \approx \frac{0.305 D \lambda}{R_L}$$
where $R_T$ is the radius of the spot at the target, $D$ is the distance to the target, $\lambda$ is the wavelength of the emitted radiation and $R_L$ is the radius of the emitting element. Size of the spot scales linearly with wavelength. If your device spits out millimetre waves (~1mm wavelength) then at the same range it will have a thousand times larger spot than a 1μm IR laser. Alternatively, to get the same power density at the target, the target either needs to be a thousand times closer, or the emitting element needs to be a thousand times bigger. That's why most people go for lasers as weapons. Also they're more awesome, because lasers. Pew pew!
Now, that's not entirely the end of the world. One thing we can do with microwaves that we can't do with visible light (right now) is make a phased array of emitters, which is of course exactly what your AESA is. This means that if you can build each emitting element cheaply enough, you can just plate your entire hull with the damn things. Omnidirectional beam, biggest possible aperture, no mucking about with turrets or mirrors or waveguides or any of that nonsense. Sure, you might lose some of the emitters to micrometeors or enemy weapon fire, but that doesn't matter because they have to scour your hull clean to fully turn the damn thing off. With a bit of cunning you can fire your microwave beams in phase with one or more friendly ships, a trick somewhat harder to manage with lasers.
Secondly, if you're using this as an electronic warfare device rather than trying to blast or burn the enemy, you can get away with an order of magnitude lower power density at the target. Electronics frazzle easily. Refractory armour does not. Scifi with space battles isn't that interested in weapons that don't make people go foom (brief honourable mention for Banks' effectors) so such things are unlikely to ever get centre stage.
Thirdly, microwave generation tends to be higher efficiency than laser generation. Stuff like gyrotrons have been around for years, and have already hit >60% efficiency at quite serious sustained power levels approaching megawatts. We still don't really have laser technology that can claim the same thing. Low efficiency means lots of heat and requires silly big power plants, which means more heat. Microwave ships need smaller heatsinks.
However, I am wondering is a device of this kind of power feasible for a somewhat realistic low end torchship
Even the smallest, weediest torchship requires a monstrously powerful nuclear engine and significantly higher spacefaring technology that we have now. Quite frankly, using microwaves instead of a laser burn death kill beam is weirdly restrained. I wouldn't sweat it.