docs(README): restore interactive examples and doctest coverage

why: The refreshed README removed valuable interactive examples that
help users learn the API through hands-on experimentation.

what:
- Restore ptpython/ipython REPL tips for exploring the API
- Add tmuxp shell shortcut tip for power users
- Restore doctest examples: session/window control, pane splitting
- Add capture-pane output example with doctest +SKIP
- Add hierarchy traversal examples (pane.window.session)
- Add architecture/about link to project links
- Emphasize The Tao of tmux book link
- Remove duplicate "Raw tmux when you need it" section
- All 12 README doctests pass via `uv run pytest README.md --doctest-glob="*.md"`

Author: tony

README.md

@@ -82,27 +82,136 @@ libtmux = "0.49.*"
 
 ## 🚀 Quickstart
 
-Create and drive a tmux session entirely from Python.
+### Open a tmux session
+
+First, start a tmux session to connect to:
+
+```console
+$ tmux new-session -s foo -n bar
+```
+
+### Pilot your tmux session via Python
+
+Use [ptpython], [ipython], etc. for a nice REPL with autocompletions:
+
+```console
+$ pip install --user ptpython
+$ ptpython
+```
+
+Connect to a live tmux session:
 
 ```python
-import libtmux
-import time
+>>> import libtmux
+>>> svr = libtmux.Server()
+>>> svr
+Server(socket_path=/tmp/tmux-.../default)
+```
 
-# Connect to tmux (starts one if not running)
-server = libtmux.Server()
-# Unique name avoids collisions on repeated runs
-session_name = f"libtmux-demo-{int(time.time())}"
-session = server.new_session(session_name=session_name, window_name="workspace")
+**Tip:** You can also use [tmuxp]'s [`tmuxp shell`] to drop straight into your
+current tmux server / session / window / pane.
+
+[ptpython]: https://github.com/prompt-toolkit/ptpython
+[ipython]: https://ipython.org/
+[`tmuxp shell`]: https://tmuxp.git-pull.com/cli/shell.html
+
+### Run any tmux command
+
+Every object has a `.cmd()` escape hatch that honors socket name and path:
+
+```python
+>>> server = Server(socket_name='libtmux_doctest')
+>>> server.cmd('display-message', 'hello world')
+<libtmux...>
+```
+
+Create a new session:
+
+```python
+>>> server.cmd('new-session', '-d', '-P', '-F#{session_id}').stdout[0]
+'$...'
+```
+
+### List and filter sessions
+
+```python
+>>> server.sessions
+[Session($... ...), ...]
+```
+
+Filter by attribute:
+
+```python
+>>> server.sessions.filter(history_limit='2000')
+[Session($... ...), ...]
+```
+
+Direct lookup:
+
+```python
+>>> server.sessions.get(session_id=session.session_id)
+Session($... ...)
+```
+
+### Control sessions and windows
+
+```python
+>>> session.rename_session('my-session')
+Session($... my-session)
+```
+
+Create new window in the background (don't switch to it):
+
+```python
+>>> bg_window = session.new_window(attach=False, window_name="bg-work")
+>>> bg_window
+Window(@... ...:bg-work, Session($... ...))
+
+>>> session.windows.filter(window_name__startswith="bg")
+[Window(@... ...:bg-work, Session($... ...))]
+
+>>> session.windows.get(window_name__startswith="bg")
+Window(@... ...:bg-work, Session($... ...))
+
+>>> bg_window.kill()
+```
+
+### Split windows and send keys
+
+```python
+>>> pane = window.split(attach=False)
+>>> pane
+Pane(%... Window(@... ...:..., Session($... ...)))
+```
 
-window = session.active_window
-left = window.active_pane
-right = window.split_window(vertical=True)
+Type inside the pane (send keystrokes):
+
+```python
+>>> pane.send_keys('echo hello')
+>>> pane.send_keys('echo hey', enter=False)
+>>> pane.enter()
+Pane(%... ...)
+```
 
-# Send commands to panes
-left.send_keys("vim", enter=True)
-right.send_keys("htop", enter=True)
+### Capture pane output
 
-print(f"✅ Session ready. Attach with: tmux attach -t {session_name}")
+```python
+>>> pane.clear()
+Pane(%... ...)
+>>> pane.send_keys("echo 'hello world'", enter=True)
+>>> pane.cmd('capture-pane', '-p').stdout  # doctest: +SKIP
+["$ echo 'hello world'", 'hello world', '$']
+```
+
+### Traverse the hierarchy
+
+Navigate from pane up to window to session:
+
+```python
+>>> pane.window
+Window(@... ...:..., Session($... ...))
+>>> pane.window.session
+Session($... ...)
 ```
 
 ## Core concepts
@@ -132,15 +241,6 @@ pane.send_keys("echo 'hello from libtmux'", enter=True)
 | libtmux | Python API over tmux       | Programmatic control, automation, testing          |
 | tmuxp   | App on top of libtmux      | Declarative tmux workspaces from YAML / TOML       |
 
-## Raw tmux when you need it
-
-```python
-server = libtmux.Server(socket_name="libtmux_doctest")
-result = server.cmd("display-message", "hello world")
-print(result.stdout)      # ['hello world']
-print(result.returncode)  # 0 on success
-```
-
 ## Testing & fixtures
 
 - pytest plugin provides fresh tmux server/session/window/pane fixtures
@@ -158,21 +258,23 @@ print(result.returncode)  # 0 on success
 
 - Docs: [docs]
 - API reference: [api]
+- Architecture: [architecture]
 - Changelog: [history]
 - Migration notes: [migration]
 - Issues: [issues]
 - Test coverage: [coverage]
 - Releases: [releases]
 - License: [license]
 - Support: [support]
-- The Tao of tmux book: [tao]
+- **[The Tao of tmux][tao]** — deep-dive book on tmux fundamentals
 
 ## Contributing & support
 
 Contributions are welcome. Please open an issue or PR if you find a bug or want to improve the API or docs. If libtmux helps you ship, consider sponsoring development via [support].
 
 [docs]: https://libtmux.git-pull.com
 [api]: https://libtmux.git-pull.com/api.html
+[architecture]: https://libtmux.git-pull.com/about.html
 [history]: https://libtmux.git-pull.com/history.html
 [migration]: https://libtmux.git-pull.com/migration.html
 [issues]: https://github.com/tmux-python/libtmux/issues