I've been attempting the same thing and it is painful to say the least.
I'm able to use MediaRecorder to record video across Chrome, Firefox, Edge, and Safari. BUT the resulting videos do not playback on all browsers.
Safari - records in mp4 and mp4 will playback on all browsers
Chrome & Edge - I'm recording with mimeType: "video/webm;codecs=vp9"
, which will playback on Chrome, Firefox, and Edge, but not Safari.
Firefox - I'm using the default. It will playback on Chrome, Firefox, and Edge, but not Safari.
Supposedly Safari will playback webm with macOS Big Sur 11.3. I need to upgrade to test this.
Unfortunately webm is still not supported by iOS, so I'm looking into the Cloudconvert API to convert webm videos to mp4 before storing in S3.
Other suggestions welcome.