feat: add the Organization browser playground

[dodok8]

Objective

Add a minimal browser playground that demonstrates the Organization schema and query workflow.

Motivation

The browser API needs one concrete, interactive proof that users can understand and maintain. A focused Organization example is sufficient; a general database IDE is not.

Expected outcome

Users can open the playground, initialize an in-memory database, inspect and edit a representative query, run it, view nested results, and reset the example.

Scope

• Depends on feat: expose browser APIs through WASM and TypeScript #89.
• Define the smallest useful playground workflow and states.
• Add the SolidStart site application if it does not yet exist.
• Initialize the in-memory database with the Organization schema and seed data.
• Provide a query editor, run action, nested result display, error display, and reset action.
• Exercise the private TypeScript browser package rather than bypassing it.
• Add focused browser tests for the complete user flow.

Related specifications and plans

• spec/schema.md
• spec/query.md
• The browser API introduced by feat: expose browser APIs through WASM and TypeScript #89

Boundaries

• Do not build a general SQL console, schema editor, database explorer, or persistence layer.
• Do not add authentication, sharing, collaboration, or saved examples.
• Keep one representative Organization example.

Acceptance criteria

• The playground workflow and UI states are documented.
• Opening the playground initializes the Organization schema and deterministic seed data in memory.
• Users can edit and run the representative query.
• Nested results and structured errors are readable in the browser.
• Reset restores the initial database and query state.
• A browser test covers initialization, execution, result display, error display, and reset.

Branch

Use issue-<issue-number>-organization-playground.

Checks

• Install dependencies with the frozen lockfile.
• Run TypeScript checks.
• Run the playground browser tests.
• Build the SolidStart application for production.