Is there anyway to embed close captioning to audio-only files? (e.g. podcast)

There are MP3 metadata extensions to embed timestamped "lyrics", but I don't know if any podcast player supports those.

The HTML audio tag is quite limited, hence a million solutions to the problem.

However the video tag supports WebVTT subtitles (and plain audio tracks) which is quite close to SRT, so it should be possible without any kind of proprietary/custom solution.

It should be possible to create an MKV file like this but I don't know what media player support is like. If it doesn't work then I guess you're stuck with the stupidly common dummy video thing (where the video content is just black or a single image like the album cover).

I seem to remember old iPods having a feature where you could switch to the lyrics but it wasn't in time with the song.

https://iandevlin.com/blog/2015/12/html5/webvtt-and-audio/