Thank you @aidenlx for this very useful plugin ! It works great for me with .mp4 files but fails with .webm files.
Here is what the html source looks like for the audio element. It seems that the media-fragment syntax has not been added at the end of the file path inside the audio tag.
<span alt="Recording 20210327113219.webm > t=6" src="Recording 20210327113219.webm#t=6" class="internal-embed media-embed is-loaded">
<audio controls="" src="app://local/C%3A%5CTemp%5CRecording%2020210327113219.webm?1618008194520">
</audio>
</span>
And for the video element, the media fragment is effectively here.
<span alt="20180625_013222.mp4 > t=5,15" src="20180625_013222.mp4#t=5,15" class="internal-embed media-embed is-loaded">
<video controls="" src="app://local/C%3A%5CTemp%5C20180625_013222.mp4?1618006957050#t=5,15">
</video>
</span>