Brake pedal slowly goes to the floor when brakes applied, and engine is running

Yes. This can be an ABS issue however, we need to start with checking all base brakes operation as it appears the issue changed when you changed the master.

What I would do first is cap all the lines coming from the master cylinder with bolts that fit (make sure they are the same depth as the line nuts so they don't bottom out. Then you press the brakes and make sure you have a hard pedal and it doesn't drop.

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

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

If it doesn't drop then the master cylinder is not the issue. At that point, start hooking the lines back on one at a time and see when the pedal starts dropping again.

I suspect you are correct but we need to eliminate a base brake issue and this is the best way to do this.

The only thing that would change this is if your vehicle is set up as the Taurus which is the USA version of this.

Basically the master on the Taurus has two lines that route to the ABS and then out to the wheels.

I would suggest still starting with the master but then you will need to move onto the ABS lines to find out if it is in the pump. Basically you just need to move through the system until you bring in the component that is causing the pedal to drop.

Let me know what questions you have. Thanks