fix(coach): lock the reasoning select while a change saves

The provider and model selects in the Coach's settings already lock while
a write is in flight; the reasoning select did not, so a second PATCH
could race the first and one change could be lost.

src/components/insights/coach-panel/__tests__/coach-settings-overlay.test.tsx

@@ -107,6 +107,17 @@ describe("<CoachSettingsBody>", () => {
     expect(html).not.toMatch(/type="password"/);
   });
 
+  it("locks the reasoning select while a change is saving", async () => {
+    // Two writes in flight at once could land out of order and lose one;
+    // the provider and model selects already lock, the reasoning one too.
+    const source = (await import("node:fs")).readFileSync(
+      new URL("../coach-model-picker.tsx", import.meta.url),
+      "utf8",
+    );
+    const field = source.match(/<ReasoningEffortField[\s\S]*?\/>/)?.[0];
+    expect(field).toMatch(/disabled=\{busy\}/);
+  });
+
   it("names the data section so a deep link can land on it", () => {
     const html = render(<CoachSettingsBody />);
     expect(html).toMatch(

src/components/insights/coach-panel/coach-model-picker.tsx

@@ -343,6 +343,7 @@ export function CoachModelPicker() {
         <ReasoningEffortField
           id="coach-quick-reasoning"
           value={reasoning.value}
+          disabled={busy}
           onChange={(next) => patchProvider.mutate({ [reasoning.field]: next })}
         />
       ) : null}

src/components/settings/ai/reasoning-effort-field.tsx

@@ -14,10 +14,13 @@ import type { ReasoningEffort } from "./shared";
 
 export function ReasoningEffortField({
   id,
+  disabled = false,
   value,
   onChange,
 }: {
   id: string;
+  /** Locks the select while a write is in flight. */
+  disabled?: boolean;
   value: ReasoningEffort | null;
   onChange: (next: ReasoningEffort | null) => void;
 }) {
@@ -28,6 +31,7 @@ export function ReasoningEffortField({
       <NativeSelect
         id={id}
         value={value ?? ""}
+        disabled={disabled}
         onChange={(e) =>
           onChange(
             e.target.value === "" ? null : (e.target.value as ReasoningEffort),