When connecting a Playground site to Jetpack, the following error shows up:

@sergeymitr pointed out there must be some database issue in the Playground site:

Looks like the site experiences issues with the database.
The site gets registered successfully, but it’s unable to save the blog ID or connection token. Then it generates the URL to establish user connection, tries to load blog ID from the options and fails.
So it doesn’t seem to be a connection issue, rather inability to properly connect the site due to option saving issues.

Jetpack is a commercial plugin, but the error is likely related to the SQLite integration in WordPress Playground and may affect other plugins.