Align the published dependency matrix with current Hex releases for all
supported providers. This update ensures compatibility with the latest
agent_session_manager and individual provider SDKs.

Key changes:
- Upgrade agent_session_manager to 0.9.0.
- Update provider SDKs: claude_agent_sdk (~> 0.17.0), codex_sdk (~> 0.16.0),
amp_sdk (~> 0.5.0), and gemini_cli_sdk (~> 0.2.0).
- Refactor PromptRunner.Scaffold to dynamically generate provider
dependencies in Mix.install based on the base provider and per-prompt
overrides instead of using a hardcoded stale list.
- Expand example workflows to demonstrate a three-prompt setup using Claude,
Codex, and Amp across single and multi-repo configurations.
- Update documentation and getting-started guides to reflect the 0.5.0
matrix and explicit dependency requirements.
- Suppress deprecated Tesla builder warnings in configuration.
- Add unit tests for scaffolding dependency resolution logic.