With this solution inspired by Visualizations with Web Audio API, you can set minimal required decibels and detect if anything was recorded.

const MIN_DECIBELS = -45;

navigator.mediaDevices.getUserMedia({ audio: true })
  .then(stream => {
    const mediaRecorder = new MediaRecorder(stream);
    mediaRecorder.start();

    const audioChunks = [];
    mediaRecorder.addEventListener("dataavailable", event => {
      audioChunks.push(event.data);
    });

    const audioContext = new AudioContext();
    const audioStreamSource = audioContext.createMediaStreamSource(stream);
    const analyser = audioContext.createAnalyser();
    analyser.minDecibels = MIN_DECIBELS;
    audioStreamSource.connect(analyser);

    const bufferLength = analyser.frequencyBinCount;
    const domainData = new Uint8Array(bufferLength);

    let soundDetected = false;

    const detectSound = () => {
      if (soundDetected) {
        return
      }

      analyser.getByteFrequencyData(domainData); 

      for (let i = 0; i < bufferLength; i++) {
        const value = domainData[i];

        if (domainData[i] > 0) {
          soundDetected = true
        }
      }

      window.requestAnimationFrame(detectSound);
    };

    window.requestAnimationFrame(detectSound);

    mediaRecorder.addEventListener("stop", () => {
      const audioBlob = new Blob(audioChunks);
      const audioUrl = URL.createObjectURL(audioBlob);
      const audio = new Audio(audioUrl);
      audio.play();
      
      console.log({ soundDetected });
    });
  });

This code can run a function for every dialog it detects. it runs in a loop until the user stops it:

VOICE_MIN_DECIBELS      = -35;
DELAY_BETWEEN_DIALOGS   = 400;
DIALOG_MAX_LENGTH       = 60*1000;
MEDIA_RECORDER          = null;
IS_RECORDING            = false;

//startRecording:
function startRecording(){
    IS_RECORDING = true;
    record();
}

//stopRecording:
function stopRecording(){
    IS_RECORDING = false;
    if(MEDIA_RECORDER !== null)
        MEDIA_RECORDER.stop();
}

//record:
function record(){
    navigator.mediaDevices.getUserMedia({ audio: true })
    .then(stream => {
        
        //start recording:
        MEDIA_RECORDER = new MediaRecorder(stream);
        MEDIA_RECORDER.start();
        
        //save audio chunks:
        const audioChunks = [];
        MEDIA_RECORDER.addEventListener("dataavailable", event => {
            audioChunks.push(event.data);
        });
        
        //analisys:
        const audioContext      = new AudioContext();
        const audioStreamSource = audioContext.createMediaStreamSource(stream);
        const analyser          = audioContext.createAnalyser();
        analyser.minDecibels    = VOICE_MIN_DECIBELS;
        audioStreamSource.connect(analyser);
        const bufferLength      = analyser.frequencyBinCount;
        const domainData        = new Uint8Array(bufferLength);
        
        //loop:
        const time              = new Date();
        let startTime,
            lastDetectedTime    = time.getTime();
        let anySoundDetected    = false;
        const detectSound       = () => {
            
            //recording stoped by user:
            if(IS_RECORDING)
                return;

            time = new Date();
            currentTime = time.getTime();
            
            //time out:
            if(currentTime > startTime + DIALOG_MAX_LENGTH){
                MEDIA_RECORDER.stop();
                return;
            }

            //a dialog detected:
            if( anySoundDetected === true &&
                currentTime > lastDetectedTime + DELAY_BETWEEN_DIALOGS
                ){
                MEDIA_RECORDER.stop();
                return;
            }
            
            //check for detection:
            analyser.getByteFrequencyData(domainData);
            for(let i = 0; i < bufferLength; i++)
                if(domainData[i] > 0){
                    anySoundDetected = true;
                    time = new Date();
                    lastDetectedTime = time.getTime();
                }
            
            //continue the loop:
            window.requestAnimationFrame(detectSound);
        };
        window.requestAnimationFrame(detectSound);

        //stop event:
        MEDIA_RECORDER.addEventListener('stop', () => {
            
            //stop all the tracks:
            stream.getTracks().forEach(track => track.stop());
            if(!anySoundDetected) return;
            
            //send to server:
            const audioBlob = new Blob(audioChunks, {'type': 'audio/mp3'});
            doWhateverWithAudio(audioBlob);
            
            //start recording again:
            record();

        });

    });
}

//doWhateverWithAudio:
function doWhateverWithAudio(audioBlob){

    //.... send to server, downlod, etc.

}