example: add C mouse encoding example

Add a new c-vt-mouse-encode example that demonstrates how to use the
mouse encoder C API. The example creates a mouse encoder configured
with SGR format and normal tracking mode, sets up terminal geometry
for pixel-to-cell coordinate mapping, and encodes a left button press
event into a terminal escape sequence.

Mirrors the structure of the existing c-vt-key-encode example. Also
adds the corresponding @example doxygen reference in vt.h.

include/ghostty/vt.h

@@ -43,6 +43,7 @@
  * Complete working examples:
  * - @ref c-vt/src/main.c - OSC parser example
  * - @ref c-vt-key-encode/src/main.c - Key encoding example
+ * - @ref c-vt-mouse-encode/src/main.c - Mouse encoding example
  * - @ref c-vt-paste/src/main.c - Paste safety check example
  * - @ref c-vt-sgr/src/main.c - SGR parser example
  * - @ref c-vt-formatter/src/main.c - Terminal formatter example
@@ -59,6 +60,11 @@
  * into terminal escape sequences using the Kitty keyboard protocol.
  */
 
+/** @example c-vt-mouse-encode/src/main.c
+ * This example demonstrates how to use the mouse encoder to convert mouse events
+ * into terminal escape sequences using the SGR mouse format.
+ */
+
 /** @example c-vt-paste/src/main.c
  * This example demonstrates how to use the paste utilities to check if
  * paste data is safe before sending it to the terminal.

include/ghostty/vt/mouse.h

@@ -24,6 +24,90 @@
  *    - Free the event with ghostty_mouse_event_free() or reuse it.
  * 4. Free the encoder with ghostty_mouse_encoder_free() when done.
  *
+ * For a complete working example, see example/c-vt-mouse-encode in the
+ * repository.
+ *
+ * ## Example
+ *
+ * @code{.c}
+ * #include <assert.h>
+ * #include <stdio.h>
+ * #include <ghostty/vt.h>
+ *
+ * int main() {
+ *   // Create encoder
+ *   GhosttyMouseEncoder encoder;
+ *   GhosttyResult result = ghostty_mouse_encoder_new(NULL, &encoder);
+ *   assert(result == GHOSTTY_SUCCESS);
+ *
+ *   // Configure SGR format with normal tracking
+ *   ghostty_mouse_encoder_setopt(encoder, GHOSTTY_MOUSE_ENCODER_OPT_EVENT,
+ *       &(GhosttyMouseTrackingMode){GHOSTTY_MOUSE_TRACKING_NORMAL});
+ *   ghostty_mouse_encoder_setopt(encoder, GHOSTTY_MOUSE_ENCODER_OPT_FORMAT,
+ *       &(GhosttyMouseFormat){GHOSTTY_MOUSE_FORMAT_SGR});
+ *
+ *   // Set terminal geometry for coordinate mapping
+ *   ghostty_mouse_encoder_setopt(encoder, GHOSTTY_MOUSE_ENCODER_OPT_SIZE,
+ *       &(GhosttyMouseEncoderSize){
+ *           .size = sizeof(GhosttyMouseEncoderSize),
+ *           .screen_width = 800, .screen_height = 600,
+ *           .cell_width = 10, .cell_height = 20,
+ *       });
+ *
+ *   // Create and configure a left button press event
+ *   GhosttyMouseEvent event;
+ *   result = ghostty_mouse_event_new(NULL, &event);
+ *   assert(result == GHOSTTY_SUCCESS);
+ *   ghostty_mouse_event_set_action(event, GHOSTTY_MOUSE_ACTION_PRESS);
+ *   ghostty_mouse_event_set_button(event, GHOSTTY_MOUSE_BUTTON_LEFT);
+ *   ghostty_mouse_event_set_position(event,
+ *       (GhosttyMousePosition){.x = 50.0f, .y = 40.0f});
+ *
+ *   // Encode the mouse event
+ *   char buf[128];
+ *   size_t written = 0;
+ *   result = ghostty_mouse_encoder_encode(encoder, event,
+ *       buf, sizeof(buf), &written);
+ *   assert(result == GHOSTTY_SUCCESS);
+ *
+ *   // Use the encoded sequence (e.g., write to terminal)
+ *   fwrite(buf, 1, written, stdout);
+ *
+ *   // Cleanup
+ *   ghostty_mouse_event_free(event);
+ *   ghostty_mouse_encoder_free(encoder);
+ *   return 0;
+ * }
+ * @endcode
+ *
+ * ## Example: Encoding with Terminal State
+ *
+ * When you have a GhosttyTerminal, you can sync its tracking mode and
+ * output format into the encoder automatically:
+ *
+ * @code{.c}
+ * // Create a terminal and feed it some VT data that enables mouse tracking
+ * GhosttyTerminal terminal;
+ * ghostty_terminal_new(NULL, &terminal,
+ *     (GhosttyTerminalOptions){.cols = 80, .rows = 24, .max_scrollback = 0});
+ *
+ * // Application might write data that enables mouse reporting, etc.
+ * ghostty_terminal_vt_write(terminal, vt_data, vt_len);
+ *
+ * // Create an encoder and sync its options from the terminal
+ * GhosttyMouseEncoder encoder;
+ * ghostty_mouse_encoder_new(NULL, &encoder);
+ * ghostty_mouse_encoder_setopt_from_terminal(encoder, terminal);
+ *
+ * // Encode a mouse event using the terminal-derived options
+ * char buf[128];
+ * size_t written = 0;
+ * ghostty_mouse_encoder_encode(encoder, event, buf, sizeof(buf), &written);
+ *
+ * ghostty_mouse_encoder_free(encoder);
+ * ghostty_terminal_free(terminal);
+ * @endcode
+ *
  * @{
  */