Do the materials dictate the ‘flavor or quality or reliability?Yes.
A capacitor stores current for when the audio signal needs it, correct?Not in the case of a coupling capacitor. Its used to block DC from one gain stage to the succeeding stage of gain while passing the audio signal at the same time.
We use the Teflon copper foil capacitors as they are simultaneously reliable and musical. Paper and oil parts are very musical, but they can develop a slight electrical leakage over time which can lead to reliability problems in the gear in which they are installed. That is why we don't use them.
The Stratos has balanced inputs and so can benefit from a balanced preamp. The trick here is that the HT stuff would be an input to the preamp, but you might also have other sources like a CDP, tuner or even a turntable that you use with the television turned off. In that case a preamp will be useful; if you only plan to use the HT as your only source there's not much point in getting an additional preamp as it will be an extra block in the signal chain that you don't need.
Now there are HT processors that are designed to work as a signal source rather than as the preamp itself; if that is what you get then the preamp makes sense. In such a situation you wouldn't need an HT bypass.