And again, not throwing any codes/lights on the dash? It's worth connecting a reader even if there are no lights just to confirm there are no pending codes. I'd do this right after reproducing the issue just to make sure.
Have you ever routed in oil catch cans, and if so, how long ago? If not, are your PCV and valve cover ventilation still routed the stock orientation? (Valve cover to intake, PCV to throttle body)
Have you ever pulled the throttle body and intake manifold? Carbon and oil residue buildup can be a massive problem on these engines, especially without catch cans. If you're comfortable with it, I would recommend pulling both and cleaning them out. This will also allow you to inspect the intake valves to see carbon buildup on the valves and intake runners. If this is sufficiently built up, it could cause the trouble with your idle. The extra load from the power steering draw on the alternator is putting extra load on the crankshaft and slowing the engine, and air can't get into the engine fast enough to keep it running at the correct idle. This is another one of those "you'll probably be glad you did it anyway" even if it's not the root cause.
If there IS an excess of buildup (post pics pls), there are a couple of options. While the intake manifold and throttle body can be cleaned out pretty easily with detergent and water, your only real options for cleaning the intake valves are either a chemical cleaner or walnut blasting.
A chemical cleaner is the easier option, where you get a friend or tool to hold the throttle at ~2500 RPM while you spray it into the throttle body in bursts to keep from stalling. While I personally haven't had any issues with using a chemical cleaner, there are people on these forums like trdtoy (who knows far more about these engines than I do) who advise against using them. Additionally, they're not all that effective, especially compared to walnut blasting. That said, it may be enough to get you vehicle running better, and for less than $20.
Walnut blasting is much more effective, and much more expensive. It can be done yourself if you have an air compressor, media blaster (harbor freight has cheap ones), shopvac, something to spin the crank, and an adapter for our intake runners. You can also check if a shop can do it, but I would expect to pay a couple hundred bucks to have them do it.