Python: Fix prek runner duplication and add skills (#3791)

* Python: fix prek runner running fmt/lint in all packages on core change

When a core package file changed, run_tasks_in_changed_packages.py ran
fmt, lint, and pyright in ALL 22 packages (66 tasks). Only type-checking
tasks (pyright, mypy) need to propagate to all packages since type
changes in core affect downstream packages. File-local tasks (fmt, lint)
only need to run in packages with actual file changes.

This reduces a core-only change from 66 tasks to 24 tasks (2 local +
22 pyright).

Also adds no-commit-to-branch builtin hook to protect the main branch
from direct commits.

* Python: add agent skills extracted from AGENTS.md and coding standards

Add 5 skills to python/.github/skills/ following the Agent Skills format:
- python-development: coding standards, type annotations, docstrings, logging
- python-testing: test structure, fixtures, running tests, async mode
- python-code-quality: linting, formatting, type checking, prek hooks, CI
- python-package-management: monorepo structure, lazy loading, versioning
- python-samples: sample structure, PEP 723, documentation guidelines

* Python: deduplicate AGENTS.md and instructions with agent skills

* updated skills

* fixes from review

* Python: increase timeout for web search integration test

python/.github/skills/python-package-management/SKILL.md

@@ -0,0 +1,103 @@
+---
+name: python-package-management
+description: >
+  Guide for managing packages in the Agent Framework Python monorepo, including
+  creating new connector packages, versioning, and the lazy-loading pattern.
+  Use this when adding, modifying, or releasing packages.
+---
+
+# Python Package Management
+
+## Monorepo Structure
+
+```
+python/
+├── pyproject.toml              # Root package (agent-framework)
+├── packages/
+│   ├── core/                   # agent-framework-core (main package)
+│   ├── azure-ai/               # agent-framework-azure-ai
+│   ├── anthropic/              # agent-framework-anthropic
+│   └── ...                     # Other connector packages
+```
+
+- `agent-framework-core` contains core abstractions and OpenAI/Azure OpenAI built-in
+- Provider packages extend core with specific integrations
+- Root `agent-framework` depends on `agent-framework-core[all]`
+
+## Dependency Management
+
+Uses [uv](https://github.com/astral-sh/uv) for dependency management and
+[poethepoet](https://github.com/nat-n/poethepoet) for task automation.
+
+```bash
+# Full setup (venv + install + prek hooks)
+uv run poe setup
+
+# Install/update all dependencies
+uv run poe install
+
+# Create venv with specific Python version
+uv run poe venv --python 3.12
+```
+
+## Lazy Loading Pattern
+
+Provider folders in core use `__getattr__` to lazy load from connector packages:
+
+```python
+# In agent_framework/azure/__init__.py
+_IMPORTS: dict[str, tuple[str, str]] = {
+    "AzureAIAgentClient": ("agent_framework_azure_ai", "agent-framework-azure-ai"),
+}
+
+def __getattr__(name: str) -> Any:
+    if name in _IMPORTS:
+        import_path, package_name = _IMPORTS[name]
+        try:
+            return getattr(importlib.import_module(import_path), name)
+        except ModuleNotFoundError as exc:
+            raise ModuleNotFoundError(
+                f"The package {package_name} is required to use `{name}`. "
+                f"Install it with: pip install {package_name}"
+            ) from exc
+```
+
+## Adding a New Connector Package
+
+**Important:** Do not create a new package unless approved by the core team.
+
+### Initial Release (Preview)
+
+1. Create directory under `packages/` (e.g., `packages/my-connector/`)
+2. Add the package to `tool.uv.sources` in root `pyproject.toml`
+3. Include samples inside the package (e.g., `packages/my-connector/samples/`)
+4. Do **NOT** add to `[all]` extra in `packages/core/pyproject.toml`
+5. Do **NOT** create lazy loading in core yet
+
+### Promotion to Stable
+
+1. Move samples to root `samples/` folder
+2. Add to `[all]` extra in `packages/core/pyproject.toml`
+3. Create provider folder in `agent_framework/` with lazy loading `__init__.py`
+
+## Versioning
+
+- All non-core packages declare a lower bound on `agent-framework-core`
+- When core version bumps with breaking changes, update the lower bound in all packages
+- Non-core packages version independently; only raise core bound when using new core APIs
+
+## Installation Options
+
+```bash
+pip install agent-framework-core          # Core only
+pip install agent-framework-core[all]     # Core + all connectors
+pip install agent-framework               # Same as core[all]
+pip install agent-framework-azure-ai      # Specific connector (pulls in core)
+```
+
+## Maintaining Documentation
+
+When changing a package, check if its `AGENTS.md` needs updates:
+- Adding/removing/renaming public classes or functions
+- Changing the package's purpose or architecture
+- Modifying import paths or usage patterns