I wrote a sort of toy version of this a little while ago using Vosk and a variety of TTS engines, and the solution that worked mostly-well was to have a buffer that waited for audio that filled until a pause of so many seconds, then it sent that to the LLM.

With the implementation of tools for GPT, I could see a way to having the model check if it thinks it received a complete thought, and if it didn't, send back a signal to keep appending to the buffer until the next long pause. The addition of a longer "pregnant pause" timeout could have the model check in to see if you're done talking or whatever.