My code still exists in the desktop source[1] but essentially what you need to do is convert an srt to vtt [2] file and start a local http server that will serve the VTT file [3] and point the Chromecast to that

[1] - https://github.com/popcorn-official/popcorn-desktop/blob/dev...

[2] - https://github.com/popcorn-official/popcorn-desktop/blob/dev...

[3] - https://github.com/popcorn-official/popcorn-desktop/blob/dev...

Isn't it possible to "burn" the subtitles on to the video file somehow, maybe with ffmpeg? So they're there permanently.

Yes but it wouldn't be ideal since you wouldn't be able to turn them on and off, or switch between multiple subtitles.

yes, the container formats such as MP4 and Matroshka support this.

Also, it can be definitely done with ffmpeg.

Not Popcorn Time, but I've had great experience using Airflow (airflow.app) for streaming video to Chromecast. Among other things, it handles subtitles quite well.

Yes, a great app, it does OCR on subtitles that are stored as images and converts to a Chromecast compatible text format so it is incredibly powerful.