Is it possible to export configuration from Apple's macOS Stocks app?
To be perfectly candid, the Stocks App and related iOS widgets are, quite frankly, not up to par.
There are many, better apps available, especially if you want to share your watch lists with others.

Your brokerage's trading app will usually allow the sharing or exporting of watch lists. Think or Swim actually has the ability to publish (Tweet) your watch list out.  You can export to CSV as well.

Excel supports &quot;pulling in&quot; of live stock price data. Nothing beats an actual spreadsheet for importing/exporting data.

Free/Paid apps on the App Store have much more functionality. For instance StockSpy has all these features including sync between multiple devices and a richer experience.

Financial Websites like Marketwatch have the ability to import/export their financial data.