Perusall's player for YouTube videos will automatically enable the display of captions when they are provided by YouTube. (For third-party apps like Perusall, YouTube will only display captions for videos when the video creator has uploaded captions to YouTube; YouTube's automatically-generated captions cannot be displayed outside of YouTube.)
For videos from other sources, or for podcasts, Chrome's "Live Captions" feature will provide live captioning for both video and audio played in Perusall. To enable this feature in Chrome (it is available in Chrome 89 or higher), navigate to Advanced > Accessibility in Chrome's settings/preferences and enable the Live Captions option. Once enabled, captions will be displayed automatically for any audio or video content in any Perusall course.