
I finally tested it successfully:
"Substital" is an add-on for Firefox and Chrome that allows you to display captions / subtitles in nearly any video that you can see on a website, either by searching for it on OpenSubtitles or by loading a caption file from your device locally.
This way you can, for example, watch an old show's episode on archive.org and add a local SRT file so the video gets captions.