I don't feel like I fully saw this explained yet:

Home Assistant itself is what provides the voice "stack" in the form of "Assistant" definitions. You can have multiple, which require defining a speech-to-text provider, a text-to-speech provider, and a langauge processing provider (agent).

By default for that last one it's Home Assistant, but LLMs can be selected too. The STT and TTS providers can be Home Assistant Cloud, which uses Azure Speech for both services. You can also install (Faster-)Whisper and Piper add-ons/apps for STT and TTS, respectively, in HA OS. (Or run them on a separate system, like in my case I use the GPU in my server since HA runs on its own micro PC).

This allows defining multiple voice "stacks" at once, so you could, for instance, have one wake word on a given device be for one pipeline for home commands, and another that just talks to an LLM.

Crucially, these do not replace the voice stacks for a Google Home/Nest or Echo device (without the hardware replacements mentioned). Those still go to their respective cloud servers for processing, not locally.

The Voice PE device is largely referred to as a "voice satellite", which is apt -- it is an extension of sorts to your existing stack. It is a device you can put somewhere convenient, like a bedside or coffee table, that is like a voice connection, sending your voice to Home Assistant for Home Assistant to process using the selected means for the pipeline active, and respond in TTS the same. It's a microphone and speaker with wifi, effectively, and that's all, as others have said.

I'm not sure I follow what you mean by "premium" though. The Voice PE device, and similar, are ~$50-60 smart speakers just like Nest/Echo (which again also rely on external processing). If you mean having Home Assistant Cloud as a subscription service, then yes sort-of -- that would give you a TTS and STT provider.