Exploring the Web Speech API
voorhoede.nl
voorhoede.nl
But i hope in few years speech API (both synthesis and recognition) will be a solved problem with strong open source alternatives
Nuance still makes Dragon and Windscribe branded speech recognition software. Dragon was great +20 years ago. Not sure how it is now, but investigating offline speech recognition is on my agenda because Microsoft nerved theirs to push people to their online service.
https://github.com/mozilla/deepspeech
This runs completely offline and is fast enough to run even on CPUs or smaller devices. Note though that it's not as accurate as an engine that requires TPUs for inferrence in order to be real time, which Google's engine probably does. World is full of tradeoffs...
Rhasspy is fully offline and uses grammars to increase accuracy just like you said.