docs: Add compatibility matrix

why: When something breaks after an upgrade, this is the first page
users check. Saves real support time.
what:
- Create docs/reference/compatibility.md
- Document Python, tmux, dependency, MCP client, and OS compatibility
- Include transport type for each client

Author: tony

docs/reference/compatibility.md

@@ -0,0 +1,48 @@
+(compatibility)=
+
+# Compatibility
+
+## Python versions
+
+| Python | Status |
+|--------|--------|
+| 3.10 | Supported |
+| 3.11 | Supported |
+| 3.12 | Supported |
+| 3.13 | Supported |
+| 3.14 | Supported |
+| PyPy | Supported |
+
+## tmux versions
+
+| tmux | Status |
+|------|--------|
+| >= 3.2a | Supported |
+| < 3.2a | Not supported (libtmux requirement) |
+
+## Dependencies
+
+| Package | Required version |
+|---------|-----------------|
+| [libtmux](https://libtmux.git-pull.com/) | >= 0.55.0, < 1.0 |
+| [FastMCP](https://github.com/jlowin/fastmcp) | >= 3.1.0, < 4.0.0 |
+
+## MCP clients
+
+| Client | Tested | Transport |
+|--------|--------|-----------|
+| Claude Code | Yes | stdio |
+| Claude Desktop | Yes | stdio |
+| Codex CLI | Yes | stdio |
+| Gemini CLI | Yes | stdio |
+| Cursor | Yes | stdio |
+| MCP Inspector | Yes | stdio |
+
+## OS support
+
+| Platform | Status |
+|----------|--------|
+| Linux | Supported |
+| macOS | Supported |
+| WSL2 | Supported |
+| Windows (native) | Not supported (tmux requires Unix) |