But that is not an option, without putting all the complexity on the input side of your battery.
Which is another way to go, from your House bank at 12V or 24V, run an inverter to feed your existing power brick
and that can go either direct to your PC, or if you want, put a big 19V battery in parallel there, charging off your power brick. That pack runs nothing but your PC.
That pack can be bigger than your House bank if you don't need lots of storage there.
Either way of course, the total energy inputs must on average be greater than what you use.
Storage Ah just gives you more buffer to spread that average out over more days.
Between House and the 19V pack you can go DCDC instead of DCACDC with the inverter, I guess that is "simplifying" maybe a bit more energy efficient (maybe) but will likely cost more investment up front.
If anyone can show a Solar controller that can adjust output 20-21V then you are correct just using the PC pack as House getting rid of the 12/24V requirement would be great.
But no links have materialised so far here.
Maybe head over to the DIY Solar forums maybe such a unit does exist.