New 4K TV; how do I best stream audio through older integrated amp

"but 4K streams at a higher rate, correct? Any way to take advantage?"

Not correct. 4K is a video standard.  24/96 audio will get you there for stereo

unless you want to process Dolby Atmos  or similar protocol, usually via HDMI and a different digital receiver than your Moon.  

Don’t worry too much about resolution with 2 channel data rates. They are pretty low, around 48 kHz. Yes, running from your TV’s digital outs to your moon is the simplest best sounding method for your current set up.

When you are ready to step up consider an Anthem MRX 540. You can use it for all your HDMI needs, power center and surround speakers, and send your L and R to your Moon.