Add Playwright test for activating a mod with database

[mnholtz]

Create a Playwright test that effectively replaces the manual regression checklist test "Activating a mod that automatically creates or uses a database" under the "Extension Console Activation" test group: https://www.notion.so/pixiebrix/Release-Checklist-Template-6d435dbf9a464f119ac6202b05d9c3b5?pvs=4#3afe7c8fc2f84c70a6ab86a8b5c1bcc0

Acceptance Criteria

Add a Playwright test that:

• Activates a mod via the Extension console that uses a database, e.g. @pixies/misc/shared-notes-sidebar-v2
• Verify that the mod works on in the PixieBrix playground https://pbx.vercel.app/
• After merging, remove the test from the regression checklist notion template https://www.notion.so/pixiebrix/Release-Checklist-Template-6d435dbf9a464f119ac6202b05d9c3b5?pvs=4#3afe7c8fc2f84c70a6ab86a8b5c1bcc0