fix(state): metrics.turns populates from emu.context_update

Last remaining stuck-at-zero from the round-5 audit. The emu typed
handler and apply_unknown branch both extracted turn_estimate for
display_value but never wrote it to metrics.turns. SESSION METRICS
"Turns" cell was decoded from metrics.turns and stayed at the
default (0, 0) for the lifetime of every session.

Both paths now set \`metrics.turns = (turn_estimate, 3)\` where 3 is
the hardcoded ±uncertainty band the renderer expects. Typed-variant
path also gates on non-negative i64 to stay defensive against bad
wire data.

Tests: 80/0 lib green; release build clean.

Author: klaiderman

inspector/src/state.rs

@@ -1335,11 +1335,19 @@ impl AppState {
 
             // ---- per-plugin display updates ----------------------------
             Event::EmuContextUpdate(p) => {
-                let turn = p.extra.get("turn_estimate")
+                let turn_n = p
+                    .extra
+                    .get("turn_estimate")
                     .and_then(|v| v.as_i64())
+                    .filter(|n| *n >= 0)
+                    .map(|n| n as u32);
+                let turn_str = turn_n
                     .map(|n| n.to_string())
                     .unwrap_or_else(|| "?".into());
-                self.set_plugin_display("emu", format!("{turn}±3"));
+                self.set_plugin_display("emu", format!("{turn_str}±3"));
+                if let Some(n) = turn_n {
+                    self.metrics.turns = (n, 3);
+                }
                 if let Some(ctx) = p.extra.get("context_size").and_then(|v| v.as_u64()) {
                     self.push_plugin_usage("emu", ctx);
                 }
@@ -1776,13 +1784,14 @@ impl AppState {
                 // Round-3 fix A: when emu.context_update arrives via the
                 // Unknown fallback path (shape variation, downgraded enum),
                 // mirror the typed handler — bump calls, set last_event,
-                // refresh display from `turn_estimate`.
+                // refresh display from `turn_estimate`, write metrics.turns.
                 let turn = p
                     .extra
                     .get("turn_estimate")
                     .and_then(|v| v.as_u64())
-                    .unwrap_or(25);
+                    .unwrap_or(25) as u32;
                 self.set_plugin_display("emu", format!("{turn}±3 turns"));
+                self.metrics.turns = (turn, 3);
                 if let Some(idx) = self.plugin_index_by_name("emu") {
                     let plug = &mut self.plugins[idx];
                     plug.calls = plug.calls.saturating_add(1);