It appears the sleep setup cannot be downloaded on the watch w/o an iPhone. I don't have an iPhone, so I cannot track my sleep data on the Apple Watch, correct?

Watches can function without a paired iPhone.

Set up an Apple Watch for a family member -

https://support.apple.com/en-us/HT211768

This sleep function of the watch requires a paired iPhone.

M1 Mac mini, macOS 12.0.1; Watch, series 5 GPS/cellular, watchOS 8.1; iPad Pro 2nd Gen, iPadOS 15.1; iPad Air 2, iPadOS 15.1; iPhone 12 Pro, iOS 15.1; TV 4th Gen, tvOS 15.1; HomePods, audioOS 15.1 and Airport Express w/ Airplay 2

Correct, in order for the watch to function it must be paired to an iPhone.