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Para o caso de video utilizaremos a tag track dentro da tag video

<video controls>
<source src="example.mp4" type="video/mp4">
<source src="example.webm" type="video/webm">
<track kind="subtitles" src="subtitles_es.vtt" srclang="es" label="Spanish">
</video>

Para os audios, usaremos a mesma tag, mas eh necessario um JS e div/span para apresentar a transcricao, conforme

https://stackoverflow.com/questions/23475335/subtitles-for-audio-with-track-how-to-display-the-subtitles

https://developer.mozilla.org/en-US/docs/Learn/HTML/Multimedia_and_embedding/Video_and_audio_content