Add basic Effect example extracted from wrapper repo

[subtleGradient]

Add basic Effect example extracted from wrapper repo

Run biome format and fix import sorting

[subtleGradient]

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• Add basic Effect example extracted from wrapper repo #49 👈 (View in Graphite)
• Add FileParserPlugin example for Effect AI #52 : 3 other dependent PRs (#45 , #47 , #48 )
• Add prompt-caching examples for Effect AI #44
• Add prompt-caching examples for AI SDK v5 #43 : 1 other dependent PR (#51 )
• Add FileParserPlugin example for fetch API #50
• Add prompt-caching examples for fetch API #42
• Clean slate: Remove all content except LICENSE.md and .env.sample #41
• main

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[Copilot]

Pull Request Overview

This PR adds a basic introductory example for using OpenRouter with @effect/ai and @effect/ai-openrouter, demonstrating fundamental Effect-TS patterns for AI interactions. The example was extracted from a wrapper repository and has been formatted according to the project's code style.

• Adds a new src/basic/example.ts file demonstrating Effect-TS patterns
• Includes three examples: simple text generation, stateful chat conversations, and streaming responses
• Follows existing code patterns with layer-based dependency injection and Effect.gen composition

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[Copilot]

The new basic example is not included in the package.json scripts. The current examples script only runs the prompt-caching examples. Consider updating the package.json to include this new basic example:

"scripts": {
  "examples": "bun run src/basic/example.ts && bun run src/prompt-caching/...",
  "typecheck": "tsc --noEmit"
}

Alternatively, if this is intentional, consider documenting how to run this example in the README or in a comment at the top of the file.

[louisgv]

nit: this one has more comment about effect than about OpenRouter