I think you might have air in the rack as well, depending on how long it was run with an empty reservoir/ bad pump.
But I don't know why you'd still have a bubbling, frothing reservoir after repeating the procedure. Air does eventually work itself to the surface after all. Try leaving the cap off overnight and see if the level drops at all.
Another thing I'd try is to drain and refill the system again, pouring in very slowly so you don't trap air as the fluid goes in. I'd disconnect the PS system hoses both at the PS pump and at the steering rack as well during draining & maybe pour some in at the rack before reattaching the tubes... space permitting.
Since the "correct" fluid is pricey but also sometimes hard to locate in a pinch, I have been using
Valvoline Max Life. Opinions differ on using non-OEM fluids so please read the specs, see if they match the OEM requirements and do what's comfortable for you.

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