I'd like to know if there is a search I can run, either internally or externally to the website, which brings up all pages linked between, say, English and Russian. (It's for comparative linguistic analysis).
This would be most helpful.
I would suggest grabbing a copy of the main database dump (either enwikisource or ruwikisource) and analyzing the contents of all pages using a special script. This script should scan for interwiki links to the other language edition that you need and you would be able to get your desired result. However, it is off-topic to provide a script here, you would have to ask for one at StackOverflow instead.
Note that Wikidata may be deployed to use by non-Wikipedia projects like Wikisource in the future, which may change how you find such information.