In general. High end systems like yours normally will have a separate DAC and streamer. Music management goes on from an iPad. Aurender is known for having a fantastic app. Great for exploring and creating a library. It will cateloge all tunes on local storage, on your network (NAS) and you can add all the streaming albums and tunes to it.
To get the most out of streaming you need a very high quality DAC and streamer. I highly recommend a used Audio Research DAC… perfect complement to your system. Incredibly musical and detailed. Given your budget… if I had to, I would look for a used ARC DAC and either a used Aurender N10 or drop down a level in Aurender. But long term a contemporary N10 or better. They redesigned the power supply on the N10 a couple years ago. Probably making some of the older ones a bit more affordable.
I just want to mention, I have been a long time Audio Research fan for preamps and phono stages, and Pass for amps (last x350). then over the last few years one by one I swapped my components for Audio Research… the wave of surprise and happiness that came over me at each additional ARC component was incredible. Each time the synergy clicked in. Now, with all ARC components my system is the best I have heard. My dealer’s as well… although he sells a lot of stuff that costs more and installs many custom systems of greater value.