None of the processes will remove pitting or replace bluing. But the idea is to stop any further rusting action.
This is something that you have to keep an eye on and inspect even after you complete the process the first time and are satisfied you have done a good job of it.
Any rust still present deep down in those tiny pits will still be active and keep doing what it does and can reappear.
'Arresting' the active rust is the goal while not disrupting the blued finish which is also a form of rust in itself.
It's a very nice looking revolver.
To elliminate the current rust damage. pits and marks, the piece can be carefully (re)polished to get below the damage. Then the engraving is recut as needed where the polishing effected it to bring the entire work back to it's former self.
The parts are then re-blued,,looks like hot-salt blue which was and is the most common bluing method that time and also now.
I would also recommend disassembly to peek inside and check for any rusting/pitting on the inside surfaces.
Sometimes the interior foam composition linings that deteriorate and cause rusting can give off gases that circulate. That can cause problems inside as well.