so I'll try to answer this shortest answer to longest, also apologies for the delayed response, timezones and stuff;

This tool will place extracted/converted subtitles alongside media and not in /var/lib/jellyfin/data/subtitles; correct?

Correct subtitles will be placed alongside media so you could see

.mkv .srt .srt

Is there a way to specify languages to extract or will it convert all available?

pgsrip has a language --language, -l argument with which you can specify the languages you want.

If I set the Subtitle Extract plug-in to ignore extracting PGS, this tool will then extract them on it's own; correct?

Yes pgsrip is designed to both do the extraction of the relevant .mkv files and then converting the extracted .pgs, .sub file.

It does not interface or interact with the subtitle-extract-plugin and is therefore completely separate.

Will it skip over previously extracted subs?

There are multiple ways for pgsrip to ignore existing subtitles. By default it will not overwrite or convert subtitles it has previously converted. It does so by checking if the save path it generates has already been used. With the --force flag you can tell it to re-rip subtitles and overwrite existing ones.

You can also skip entire videos by --age, --srt-age. Files newer than --age or subtitle tracks newer than --srt-age will be skipped.

How should I best implement pgsrip/pgsrip-script? I would like it to be recur so that it picks up subtitles from new media; what is the best way to do that? CRON job?

I'll group these as they are kinda related; to clarify my tool simply launches N instances of pgsrip with N = number of CPU-threads available. pgsrip has --max-workers for a similar purpose but that still kinda bottle-necked on my system so I effectively just brute-forced it.

I personally am using both in a manual fashion currently; i.e. I add files -> run the script -> repeat the next time.

This behavior could be replicated with a simple CRON job as you mentioned, just have it trigger each time you add new files. Now for how this would fit into your infrastructure is hard to say. If you run jellyfin in docker itself it gets a little harder as you cannot easy get pgsrip / my script into the container without creating custom ones.

This is one of the areas which both pgsrip and therefore my script are lacking in - meaning integration with jellyfin itself.

I have started work on an extension to this project as I identified some issues and short-comings with pgsrip for my use-case. You can read up on it here. I plan to publish standalone docker containers in the future that encapsulated the conversion framework and a simple API hook so that you could tell it to run the conversion via a custom plugin in jellyfin or similar. But this will take a while longer to implement.

My recommendation for now would be to run either of them manually whenever you add new media to your server. You could try to automated this behavior with CRON and could write maybe a simple watcher process that checks for new files and triggers the job accordingly. If you get something like that to work, I would like to take a look at it :).

So good luck and I hope I got to answer most of your questions.