Using the `test.all_types` document from compass data sets let's have a test that runs the playground controller against a real database and:

• Inserts the all_types document.
• Finds the inserted document.
• Checks that the found document is what we expect.

This would catch errors like what caused VSCODE-473 and prevent regressions.

From what I can tell we don't currently have a test that fully runs a playground against a database and checks the result, so this would be valuable to do sooner.