Brakes not working properly after replacing the brake pads and calipers?

So, do you have a good brake pedal, or does it go to the floor? The first thing to mind is you have air in the system, the second thing is what type of brake pads did you use? I would use only semi metallic. Can you please shoot a quick video with your phone so I can tell for sure what's going on. You can upload it here with your response.

Absolutely, but not the power booster. The booster simply makes it easier to push the brake pedal. It isn't involved with how far the pedal is pushed.

Most competent do-it-yourselfers, and even some inexperienced mechanics, bleed the air out of the hydraulic systems by pressing the brake pedal repeatedly, (pedal-bleeding). The problem comes from pressing it all the way to the floor. Crud and corrosion build up in the lower halves of the bores in the master cylinder where the pistons don't normally travel. By pressing the brake pedal to the floor, whether bleeding or when surprised by a ruptured brake hose, the rubber lip seals are run over that crud which can rip them. That results in a slowly sinking brake pedal, and that commonly takes two or three days to show up. If only one of those seals tears, you'll still have half of the brakes working, but the pedal will be very low. The red "Brake" warning light will turn on too. That warning light will usually not turn on when both seals are torn.

The only bleeding system I've used for decades is "gravity-bleeding". No helper is needed, and there's little chance of damaging the master cylinder. The next problem, regardless if you installed new calipers or if you simply pushed the pistons into the caliper housings to make room for the new, thicker pads, those pistons have to be run out to adjust them. That's done by pressing the brake pedal multiple times until a high, hard pedal is achieved, and that too will make it possible to push the brake pedal to the floor the first few times. That's enough to rip the lip seals. Professionals know to never push the pedal over halfway to the floor, unless the master cylinder is less than about a year old.

The next potential problem occurs if the reservoir is allowed to run empty. This can happen due to gravity when a caliper is unbolted from the rubber flex hose. If your vehicle has only the standard brake system, just bleed the air out at the calipers like normal. If it has anti-lock brakes, the majority of models have a hydraulic controller where air can become trapped. Since air can be compressed, that also leads to a low brake pedal. On models where that air doesn't continue down to the wheels where it can be bled out, you need a scanner that can command the ABS Computer to open a pair of valves to bleed the air from those chambers. After that is done, the air can be bled the rest of the way by normal procedures.

A simple way to prevent the reservoir from running empty when a line is open / caliper is removed, is to place a stick between the brake pedal and the driver's seat to hold the pedal down about an inch. Gravity won't be strong enough to pull brake fluid past the lip seals in the master cylinder.

When you're starting out with no air in the system, but you need to replace the master cylinder, there's a simple trick to avoid needing to bleed at the wheels. First, bench-bleed the new master cylinder line normal. Next, loosen the soft metal line nuts at the master cylinder. Unbolt the master cylinder from the power booster, pull it forward off the mounting studs, then use it as a handle to bend the steel lines upward a little. That will reduce the amount of brake fluid that runs out. Finish unbolting the lines, then bolt them to the new master cylinder. Bend the lines back down and install the master cylinder to the booster. Now loosen one line nut, then have a helper slowly press the brake pedal halfway to the floor. It should take about 15 to 20 seconds to do this. You'll see air bubbles come out by the nut. Snug that nut, THEN holler to your helper to release the pedal quickly. Loosen the nut again and do the same thing, and maybe a third time, until no air bubbles come out, then tighten that nut. Do the same procedure for the second line. Since this is a new or rebuilt master cylinder, there's no crud built up in the bottoms of the two bores, so the seals can't be damaged, but it is still good practice to tell your helper to push the pedal no further than halfway to the floor.

By pushing the brake pedal slowly, any small air bubbles will float back up as the brake fluid goes down the lines. By releasing the pedal quickly, the brake fluid rushing back up to the reservoir will wash any air bubbles along with it. No air will go down to the calipers or into the ABS hydraulic controller. If a few tiny air bubbles remain in the system, they'll be much too small to affect the feel of the brake pedal, and since air always goes up, those bubbles will get washed into the reservoir very quickly.

Here's links to some articles you may find of interest:

https://www.2carpros.com/articles/brake-pedal-goes-to-the-floor

https://www.2carpros.com/articles/how-to-bleed-or-flush-a-car-brake-system

https://www.2carpros.com/articles/brake-caliper-replacement

https://www.2carpros.com/articles/how-to-replace-a-brake-master-cylinder

Please keep me updated on your progress.

You covered all of that in your original question. Stopping the wheels when the vehicle is raised up doesn't take very much braking power. That's why a master cylinder with torn lip seals may still be able to do the job. To stop a moving small car, a master cylinder can easily be capable of developing over 2,000 psi of brake fluid pressure. A seal that has been damaged by pressing the brake pedal to the floor will leak internally, meaning the fluid is bypassing it rather than being pushed down to the brakes. What little pressure it may still be able to develop will not stop the vehicle efficiently. The repair is to replace the master cylinder.

For many models you can find rebuild kits for the master cylinder, but those are usually not a good value. Every time I've checked, those kits cost just as much or even more than the professionally rebuilt unit with a warranty.