feat(statusbar): honor $COORDS in the coordinate readout, click to cycle

The Coords pill always showed live absolute X,Y,Z, ignoring the drawing's
$COORDS (coords_mode) sysvar. Drive the readout from it:

- 0 static  — the last picked point; the readout freezes between picks.
- 1 live    — continuous absolute X,Y,Z (previous behavior, default).
- 2 polar   — distance<angle relative to the last point while a command is
              prompting for a point; absolute otherwise.

The cursor and last point are reported in the active UCS, matching the rest of
the readout. Clicking the pill cycles the mode 0→1→2→0 (CycleCoordsMode), marks
the tab dirty and echoes it; SETVAR COORDS still works. $COORDS round-trips per
drawing via acadrust's coords_mode.

Co-Authored-By: Claude Opus 4.8 <[email protected]>

src/app/mod.rs

@@ -1458,6 +1458,8 @@ pub enum Message {
     ToggleLayoutList,
     /// Close the Model/layout list dropdown.
     CloseLayoutList,
+    /// Cycle the coordinate readout mode ($COORDS): static → live → polar.
+    CycleCoordsMode,
     /// Toggle the status-bar customization menu open/closed.
     ToggleStatusBarMenu,
     /// Close the status-bar customization menu.

src/app/update/mod.rs

@@ -1541,6 +1541,26 @@ impl OpenCADStudio {
                 }
                 Task::none()
             }
+            Message::CycleCoordsMode => {
+                // $COORDS 0 (static) → 1 (live absolute) → 2 (polar) → 0.
+                let i = self.active_tab;
+                if i < self.tabs.len() {
+                    let mode = {
+                        let h = &mut self.tabs[i].scene.document.header;
+                        h.coords_mode = (h.coords_mode + 1).rem_euclid(3);
+                        h.coords_mode
+                    };
+                    self.tabs[i].dirty = true;
+                    let label = match mode {
+                        0 => "static",
+                        2 => "polar",
+                        _ => "live",
+                    };
+                    self.command_line
+                        .push_output(&format!("COORDS = {mode} ({label})"));
+                }
+                Task::none()
+            }
             Message::TogglePolar => {
                 self.polar_mode ^= true;
                 if self.polar_mode {

src/app/view/mod.rs

@@ -1303,16 +1303,21 @@ impl OpenCADStudio {
                     // drawing coordinates (paper space carries no offset), then
                     // report it in the active UCS — the readout follows the
                     // user's coordinate system, not raw WCS (no-op without UCS).
-                    let cursor_coord = {
-                        let lc = tab.last_cursor_world;
+                    let to_readout = |p: glam::Vec3| {
                         // The readout follows the active pane's UCS — model space
                         // or inside a floating viewport (no-op without a UCS).
                         if tab.editing_model_space() {
-                            tab.ucs_xform().to_ucs(lc)
+                            tab.ucs_xform().to_ucs(p)
                         } else {
-                            lc
+                            p
                         }
                     };
+                    let cursor_coord = to_readout(tab.last_cursor_world);
+                    // The last picked point (same UCS as the cursor) drives the
+                    // static ($COORDS 0) and polar ($COORDS 2) readouts.
+                    let last_coord = self.last_point.map(to_readout);
+                    let coords_mode = tab.scene.document.header.coords_mode;
+                    let picking = tab.active_cmd.is_some();
                     self.status_bar.view(
                         &self.snapper,
                         self.snap_popup_open,
@@ -1334,6 +1339,9 @@ impl OpenCADStudio {
                         scale_pill_enabled,
                         tab.scene.document.header.lineweight_display,
                         cursor_coord,
+                        coords_mode,
+                        last_coord,
+                        picking,
                         self.clean_screen,
                         tab.scene.document.header.insertion_units,
                         self.units_popup_open,