There's this react-native library react-native-voice that handles speech-to-text. I am doing the same project as you, I used it and it works after going through myriad debuggings. It works for me with the API 30, make sure to check 'Virtual microphone uses host audio input' in the microphone tab on your emulator device, to enable your computer audio. For more details, see the package repo enter link description here, the issue enter link description here, and the implementation exampleenter link description here
To walk you through, see the youtube tutorial https://www.youtube.com/channel/UCHau-Of64A57oL3EipcMpSA