feat: /api/intrinsics gives what an align outside the SDK needs

Already there: fx/fy/cx/cy and k1,k2,k3,p1,p2 of both streams, extrinsics
depth->color (rotation row-major, translation mm). Added, as new keys only:
width, height and distortion model name (an rs.distortion member) in "ir"
and "rgb", and depth_scale_m at the top. Docstring states the extrinsics
convention: p_rgb = R p_ir + t, R row-major (the SDK's is column-major).
Same keys in /api/status and /api/open, which share the payload.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

src/backend/api/routes.py

@@ -269,7 +269,13 @@ def _frame_to_dict(frame: CameraFrame, include_images: bool = True) -> dict:
 
 
 def _calibration_payload() -> dict | None:
-    """Full calibration (intrinsics + distortion + extrinsics) or None."""
+    """Full calibration (intrinsics + distortion + extrinsics) or None.
+
+    Enough to align depth to color outside the SDK: per stream width, height
+    and distortion model (rs.distortion member name), depth_scale_m (meters per
+    raw unit). extrinsics_ir_to_rgb: p_rgb = R p_ir + t, R row-major (the SDK's
+    is column-major), t in millimeters.
+    """
     if not _camera or not _camera.intrinsics:
         return None
     i = _camera.intrinsics
@@ -280,19 +286,26 @@ def _calibration_payload() -> dict | None:
     def _d(d):
         return None if d is None else {"k1": d.k1, "k2": d.k2, "k3": d.k3, "p1": d.p1, "p2": d.p2}
 
+    def _stream(name):
+        width, height = _camera.stream_sizes.get(name, (None, None))
+        return {"width": width, "height": height, "model": _camera.distortion_models.get(name)}
+
     return {
         "ir": {
             "fx": i.fx_ir, "fy": i.fy_ir, "cx": i.cx_ir, "cy": i.cy_ir,
             "distortion": _d(dir_),
+            **_stream("ir"),
         },
         "rgb": {
             "fx": i.fx_rgb, "fy": i.fy_rgb, "cx": i.cx_rgb, "cy": i.cy_rgb,
             "distortion": _d(drgb),
+            **_stream("rgb"),
         },
         "extrinsics_ir_to_rgb": None if e is None else {
             "rotation": list(e.rotation),
             "translation": list(e.translation),
         },
+        "depth_scale_m": _camera.depth_scale(),
     }