Any damage to PS system caused by short term fluid loss is unlikely.

Did you thoroughly bleed the system? (engine off, front end off the ground, turning wheel lock to lock several times, running engine and repeating)

Did you fill the system with ATF+4 or generic PS fluid?

Rough idle could be a vacuum leak, if you disconnected or damaged an old cracked hose during the work...

 

I had this same thing happen to me and drove back home. (Bad idea) I ended up having to replace the power steering rack. I now check the cooler hoses every year and replace them every five to six years if needed.

 

I'm so afraid of this happening again. I had to drive it a few blocks. How do you know the rack was bad?

 

I've driven '05 van ~100 mi with ruptured pressure line (zero power assist) and had no ill effects to steering systems...

 

Same here. My 2005 DGC SXT blew a line. I went 30 or so miles and got home. I took it easy and didn't push it hard.
Changed the hoses and the reservoir. Bleed the system, only used ATF+4. Drove for a few days, burped more air out the reservoir.

The hardest part was cleaning up the mess under the van!

 

You are probably just noticing things more and overthinking it.
No seals or pipes leaking on the rack? No leaks at all?
Any loud squealing? on sharp turns when parking/turning when cold?
Steer it lock to lock, 3 or 4 times, in a parking lot, to get rid of air.
The pump may have taken a beating and is a bit noisier. Very cold temperatures can make it noisier (squeal).
Your system basically got a flush and got rid of/dislodged some noise dampening dirt - maybe.
Put a little extra fluid (ATF+$) in the reservoir and run it for 500 miles, or so, to see if it quiets down. Keep an eye on it and document, regularly, what you find. Compare the data and report back.
What's your idle RPM? around 750?

$ = 4