Ability to use Google voice typing instead of speech to text service when making assist requests

**Is your feature request related to a problem? Please describe.**
I'm starting to grow a bit frustrated with the accuracy of faster-whisper, and the general UX around the home assistant assist microphone button.

**Describe the solution you'd like**
I would personally like to just bring up Google voice typing automatically instead when I pull up the assistant, and send the input once I'm finished.

**Describe alternatives you've considered, if any**
I just made another voice assistant for My Wear OS smartwatch within the home assistant settings that is essentially the same as the default. But does not have a speech to text service set. This setup works flawlessly to what I want because it brings up the wear OS keyboard in microphone mode, and I would love to have the same thing, but now on regular android.

**Additional context**

Start by locating the Android assist microphone flow and reviewing how speech-to-text services are selected. Compare it with the described Wear OS setup, then define the Android behavior and verify that voice input is submitted after the user finishes speaking.

Written by the indexing model from the issue text.