docs: Add comprehensive async documentation

Add first-class async documentation across README, quickstart, and API
reference to match sync documentation standards.

Created docs/api/async.md (comprehensive async API reference):
- Overview and when to use async methods
- Complete method documentation with usage examples
- Concurrent operations patterns
- Integration with async frameworks (FastAPI, aiohttp)
- Error handling patterns
- Performance characteristics and benchmarks
- Comparison table: sync vs async
- Implementation details (a' prefix convention)
- Roadmap positioning as foundation of async support

Updated README.md:
- Added "Async Support" section before "Python support"
- Practical example showing concurrent window creation
- List of all 5 async methods with descriptions
- Link to full async API documentation

Updated docs/quickstart.md:
- Added "Async Support" section before "Final notes"
- Basic async usage example
- Concurrent operations example with asyncio.gather()
- List of available async methods with cross-references
- When to use async guidance

Updated docs/api/index.md:
- Added 'async' to toctree after 'panes'

Updated API reference files:
- docs/api/servers.md: Added async methods section
- docs/api/sessions.md: Added async methods section
- docs/api/windows.md: Added async methods section
- All include cross-references to comprehensive async docs

Sphinx build: Succeeds with 62 warnings (pre-existing, not from changes)

This completes essential async documentation (Option B), providing:
✅ All source code docstrings enhanced
✅ README shows async exists and how to use it
✅ Quickstart teaches async patterns
✅ Comprehensive async API reference
✅ Navigation and discoverability
✅ First-class documentation parity with sync methods

Author: tony

README.md

@@ -246,6 +246,46 @@ Window(@1 1:..., Session($1 ...))
 Session($1 ...)
 ```
 
+# Async support
+
+libtmux provides async versions of key methods for use in async applications:
+
+```python
+import asyncio
+from libtmux import Server
+
+async def main():
+    server = Server()
+
+    # Create session asynchronously
+    session = await server.anew_session(
+        session_name="async_session",
+        start_directory="~/"
+    )
+
+    # Create windows concurrently
+    windows = await asyncio.gather(
+        session.anew_window(window_name="editor"),
+        session.anew_window(window_name="terminal"),
+        session.anew_window(window_name="logs"),
+    )
+
+    # Check session exists
+    exists = await server.ahas_session("async_session")
+    print(f"Session exists: {exists}")  # True
+
+asyncio.run(main())
+```
+
+Available async methods (using 'a' prefix convention):
+- `Server.ahas_session()` - Check if session exists
+- `Server.anew_session()` - Create new session
+- `Session.anew_window()` - Create new window
+- `Session.arename_session()` - Rename session
+- `Window.akill()` - Kill window
+
+See the [async API documentation](https://libtmux.git-pull.com/api/async.html) for details.
+
 # Python support
 
 Unsupported / no security releases or bug fixes: