fix(units): make the units selector reach what it names

The status-bar units button wrote INSUNITS, which nothing on screen reads.
INSUNITS only tells the drawing how to scale content arriving from
elsewhere, so picking a unit relabelled the drawing and changed nothing
visible — the selector looked broken because the variable it moved was
invisible.

Point the button at LUNITS instead, the setting that decides how every
coordinate and distance is written, and give the three questions the word
"units" runs together a place each:

- The button offers the five length formats, each shown beside a sample of
  itself, so Engineering and Architectural are told apart by sight.
- UNITS / DDUNITS opens a real dialog: length and angle format and
  precision, the direction angle zero points, whether positive angles run
  clockwise, and the insertion unit. Its sample comes from the same
  formatters the drawing uses, so it cannot drift from the readout.
- DWGUNITS converts. Model geometry, viewport framing, the header's length
  defaults and each dimension style's scale all move together in one undo
  step; paper space is left alone, since the sheet is still the same sheet.
  Locked layers are converted too — a half-converted drawing would be at
  two scales at once.

The coordinate readout formatted at four decimal places whatever the
drawing asked for; it now goes through the same format_length the
properties panel uses. That made the angle formats reachable in turn, so
degrees-minutes-seconds now carries the d/'/" marks that say which
convention it is, and surveyor's units are written at all.

Typed input is still plain decimal: a length the readout writes as
5'-6 1/2" cannot yet be typed back. ANGBASE and ANGDIR are stored but not
yet applied to displayed directions.

Closes #668

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

src/ui/statusbar/mod.rs

@@ -102,8 +102,8 @@ impl StatusBar {
         picking: bool,
         // True while clean-screen mode hides the ribbon and side panels.
         clean_screen: bool,
-        // Drawing units (INSUNITS) for the units pill.
-        insertion_units: i16,
+        // LUNITS — how lengths are written, for the units pill.
+        linear_format: i16,
         // True when objects are hidden by Isolate / Hide.
         isolation_active: bool,
         // Whether entity transparency is shown (Transparency pill state).
@@ -353,11 +353,13 @@ impl StatusBar {
             pills.push(
                 status_menu::menu_bar(
                     menu_tip(
-                        popup_pill(t!(crate::ui::popup::units_popup::unit_short(insertion_units))),
-                        t!("Drawing Units (INSUNITS)\nClick to change"),
+                        popup_pill(t!(crate::modules::draw::units::linear_format_short(
+                            linear_format
+                        ))),
+                        t!("Units (LUNITS)\nHow lengths are written\nClick to change"),
                         tooltip_hidden,
                     ),
-                    crate::ui::popup::units_popup::menu_entries(insertion_units),
+                    crate::ui::popup::units_popup::menu_entries(linear_format),
                     140.0,
                 )
                 .into(),
@@ -554,8 +556,15 @@ impl StatusBar {
 
 // ── Coordinate readout ────────────────────────────────────────────────────
 
+/// The readout, in the drawing's own linear units.
+///
+/// Lengths went out at four decimal places whatever the drawing asked for, so a
+/// drawing set to architectural units read its coordinates in decimals, and one
+/// asking for two places got four. `format_length` is the same helper the
+/// properties panel formats through, so both now say a length the same way.
 fn format_coords(cursor: glam::DVec3, last: Option<glam::DVec3>, mode: i16, picking: bool) -> String {
-    let abs = |p: glam::DVec3| format!("{:.4}, {:.4}, {:.4}", p.x, p.y, p.z);
+    use crate::entities::common::format_length as len;
+    let abs = |p: glam::DVec3| format!("{}, {}, {}", len(p.x), len(p.y), len(p.z));
     match mode {
         // Static: show the last picked point; the readout freezes between picks.
         0 => abs(last.unwrap_or(cursor)),
@@ -565,11 +574,14 @@ fn format_coords(cursor: glam::DVec3, last: Option<glam::DVec3>, mode: i16, pick
             (true, Some(l)) => {
                 let d = cursor - l;
                 let dist = (d.x * d.x + d.y * d.y).sqrt();
-                let mut ang = d.y.atan2(d.x).to_degrees();
-                if ang < 0.0 {
-                    ang += 360.0;
-                }
-                format!("{dist:.4} < {ang:.2}\u{b0}")
+                // Kept in 0..2pi so the readout never shows a negative bearing,
+                // then handed over in radians for AUNITS / AUPREC to format.
+                let ang = d.y.atan2(d.x).rem_euclid(std::f64::consts::TAU);
+                format!(
+                    "{} < {}",
+                    len(dist),
+                    crate::entities::common::format_angle(ang)
+                )
             }
             _ => abs(cursor),
         },