Problems with the hydraulic pump on a 2004 Civic

Good afternoon everyone, I have a problem with my 2004 Honda Civic. It has 56,000 miles. Suddenly, the power steering pump started making a bad noise. I already checked the belt, and everything is fine for leaks and air inlets. So I decided to remove the pump, inspect it, and it's not scratched; it's intact, like new. I reassembled it and added the fluid, but I noticed that even though I filled it to the correct level, it started leaking from the oil reservoir cap. What do you think the problem could be? It's always making that noise, and it's really driving me crazy.
Thanks,
I look forward to your replies.

That symptom usually means there's air in the system; you need to bleed it and it will come out because a back pressure is generated.

Good afternoon, sir. How do I perform that purge?
Could you be more explicit? Thank you.

Sorry, I thought you knew. Well, lift the vehicle by both front wheels, start the engine, and move the steering wheel from end to end, applying a little pressure when you reach the stop. This is done without the reservoir cap installed, and you refill it as needed. Be careful because sometimes you can make the mistake of putting the drive belt on incorrectly and the pump turns in the opposite direction.