There is now Aside, an unofficial Google library for adding type support, linting and unit testing to Apps Script using TypeScript, ESLint, Prettier, and Jest.

Note that as far as I can tell, to run tests in Jest on functions which remotely execute Google Apps APIs (even things like SpreadsheetApp.getActiveSpreadsheet().getSheetByName("Home").getRange("A1").getValue()), you would need to:

1. Write a test function which will run remotely and does setup, calls the function you are testing, and then outputs the result to stdout
2. Write a Jest test which will call clasp run <test_function> (see this documentation on clasp run and this SO post on calling command line functions from node) and then write assertions against the output.