Full remote input parity: forward mouse and structured key events over IPC

- New key_event/mouse_event client messages (crossterm serde) that run
  through the complete WM event handling on the server — remote clients
  get window focus, drag/resize and mouse forwarding into virtual
  terminals (SGR/UTF-8/X10) identical to standalone mode
- tui-wm -c now forwards mouse events; previously only keyboard worked
  remotely
- IPC unit tests + end-to-end integration test (tests/integration.py):
  daemon, frames, click/scroll SGR forwarding, popups, TUI-FM in a
  window — 12/12 passing
- Document the new messages in SOCKET_API.md

Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>

SOCKET_API.md

@@ -85,6 +85,44 @@ Forward raw terminal input bytes to the focused window. Bytes are hex-encoded.
 
 The example sends the bytes `0x1b 0x5b 0x41` (Up arrow).
 
+### `key_event`
+
+Forward a structured keyboard event. Unlike `input`, the event runs through
+the full window-manager event handling: global keybinds, dialogs, focus and
+PTY forwarding — exactly as if the key was pressed locally in standalone
+mode. This is what `tui-wm -c` sends for every keypress.
+
+```json
+{
+  "type": "key_event",
+  "event": { "code": { "Char": "a" }, "modifiers": "CONTROL", "kind": "Press", "state": "" }
+}
+```
+
+`code` is either `{ "Char": "<tecken>" }` or a string for special keys
+(`"Enter"`, `"Esc"`, `"Tab"`, `"Backspace"`, `"Up"`, `"Down"`, `"Left"`,
+`"Right"`, `"Home"`, `"End"`, `"PageUp"`, `"PageDown"`, `"Delete"`, ...).
+`modifiers` is a `|`-separated string of `SHIFT`, `CONTROL`, `ALT`
+(empty string = none).
+
+### `mouse_event`
+
+Forward a structured mouse event. Gives remote clients full mouse parity
+with standalone mode: window focus, title-bar drag, resize, and forwarding
+into the virtual terminals with correct SGR/UTF-8/X10 encoding and
+coordinate translation. This is what `tui-wm -c` sends for every mouse event.
+
+```json
+{
+  "type": "mouse_event",
+  "event": { "kind": { "Down": "Left" }, "column": 10, "row": 5, "modifiers": "" }
+}
+```
+
+`kind` is one of `{ "Down": <btn> }`, `{ "Up": <btn> }`, `{ "Drag": <btn> }`,
+`"Moved"`, `"ScrollUp"`, `"ScrollDown"` where `<btn>` is `"Left"`,
+`"Right"` or `"Middle"`. Coordinates are 0-based frame coordinates.
+
 ### `resize`
 
 Notify the server that the display client's terminal has been resized.