Yeah I also made a chrome extensions for this for personal use, but realized that there wasn't a good trade-off between having it sound good and getting rapid responses.

You don't want to start speaking before you get a full sentence, or the TTS will sound weird. You don't want to wait for a full sentence, because it would be too slow.

Besides that, speech recognition wasn't working well enough, and I heard (haven't tried) Whisper has the same delay problem where you again cannot stream it, but must wait for the user to have spoken for a while.