The front brake didn't activate and then seize over time onto the rotor. The brake seized, then someone at some point used pumped the lever and then it pushed the essentially seized brake so it death gripped the rotor. If your master cylinder is working, you now have the best working tool to get the pistons out so the whole assembly can be cleaned, inspected and serviced (if not damaged).
If someone were to go to a shop with just the calipers, they would just attach them to a grease gun and pump them out (essentially what the master cylinder would do but without all the grease).
The adjustment screw isn't going to relieve any of that pressure. It only controls the adjustment or alignment in relation to the rotor.
At the very least you will need a new piston seal. Maybe a new bleeder screw, pads, or a new piston if it's too pitted.
Basically you can't assess what to replace until you inspect it. You can't inspect it til you get it apart. Probably the easiest way to do it instead of trying to get the caliper off right away would be to take the wheel off. It is going to be a lot easier to remove the wheel off the caliper than the caliper off the wheel. The caliper is bolted on so it's stationary. The wheel you can unbolt and then also turn it while pulling it.
Don't unhook the master cylinder yet, you will probably need to use it to get the pistons out.