The brake pedal is soft

Yup. That is due to internal leakage past the seals.

For future reference, the main cause of this is improper bleeding procedures after performing other brake service, an external leak, or anything else that allows you to push the brake pedal all the way to the floor. Another common mistake is when someone pushes the pistons into the calipers to install new, thicker brake pads, then they have to pump the brake pedal to run the pistons back out as the final step of the service. When doing that, never push the pedal more than halfway to the floor.

Anything that allows the pedal to go down too far can damage a master cylinder that is more than about a year old. Crud and corrosion build up in the lower halves of the bores where the pistons don't normally travel. Pushing the brake pedal more than halfway down runs the lip seals over that crud and rips them. Very often that doesn't show up right away, but when it does, the most common symptom is a slowly-sinking brake pedal. Commonly within a few days the other lip seal does the same thing, then you won't have any brakes, so don't ignore this.