One-pill study chrome, toggling chat pickers, readable homework steps

UI batch from feedback:

- The study/review/exam/homework chrome is now a single 58px pill: round
  close button, title + position over the progress bar, chips (or the exam
  timer) at the far end — everything on the centre line, so nothing crowds
  the rounded corners any more. Homework guide gets the same recipe.
- The immersive feeds carry z-[45] so they paint over the app chrome (on
  /exam the header used to cover the top of the chrome), and the page chrome
  behind an open overlay (.app-header, .segmented, .tabbar) is hidden while
  the transparent overlay is up, so it can no longer ghost through the glass.
  The guide's disclaimer moved inside the overlay with it.
- Chat: the context and model chips toggle their own popover (pressed state,
  aria-expanded), opening one closes the other, a press outside closes it —
  no more being forced to pick something to get out.
- Homework: the model's plain-text step explanations/hints/verdicts keep
  their line breaks (whitespace-pre-wrap) — a step used to collapse into one
  run-on paragraph with the whole solution inside it; the guide prompt now
  says the explanation is coaching, 2-4 sentences.
- The four glacier blobs are at 25% of their old opacity (0.045 light,
  0.1 dark).

Tests: phase-2 chrome geometry + exam layering checks (62), chat desktop
picker checks (101), the standing suites all green. README: decisions 54-56,
decision 23 updated. SW -> freezmo-v44.

components/chat/Composer.tsx

@@ -26,6 +26,8 @@ export function Composer({
   online,
   scopeLabel,
   modelLabel,
+  scopeOpen,
+  modelOpen,
   onOpenScope,
   onOpenModel,
   onAttachFile,
@@ -41,6 +43,8 @@ export function Composer({
   online: boolean;
   scopeLabel: string;
   modelLabel: string;
+  scopeOpen: boolean;
+  modelOpen: boolean;
   onOpenScope: () => void;
   onOpenModel: () => void;
   onAttachFile: (file: File) => void;
@@ -156,16 +160,22 @@ export function Composer({
       <div className="mt-2 flex items-center gap-2 overflow-x-auto">
         <button
           type="button"
+          data-picker-trigger
+          aria-haspopup="dialog"
+          aria-expanded={scopeOpen}
           onClick={onOpenScope}
-          className="flex min-w-0 items-center gap-1.5 rounded-xl border border-[var(--hairline-soft)] bg-[var(--surface-sunken)] px-2.5 py-1.5 text-[12px] font-medium text-[var(--text-muted)] transition hover:text-[var(--text)]"
+          className={pickerChipClass(scopeOpen)}
         >
           <LayersIcon className="size-3.5 shrink-0" />
           <span className="max-w-[170px] truncate">{scopeLabel}</span>
         </button>
         <button
           type="button"
+          data-picker-trigger
+          aria-haspopup="dialog"
+          aria-expanded={modelOpen}
           onClick={onOpenModel}
-          className="flex min-w-0 items-center gap-1.5 rounded-xl border border-[var(--hairline-soft)] bg-[var(--surface-sunken)] px-2.5 py-1.5 text-[12px] font-medium text-[var(--text-muted)] transition hover:text-[var(--text)]"
+          className={pickerChipClass(modelOpen)}
         >
           <ChatIcon className="size-3.5 shrink-0" />
           <span className="max-w-[170px] truncate">{modelLabel}</span>
@@ -181,3 +191,16 @@ export function Composer({
     </div>
   );
 }
+
+/**
+ * Chip style for the two popover triggers (context, model). The open state
+ * reads pressed, because the same chip opens and closes its popover.
+ */
+function pickerChipClass(open: boolean): string {
+  return cn(
+    "flex min-w-0 items-center gap-1.5 rounded-xl border px-2.5 py-1.5 text-[12px] font-medium transition",
+    open
+      ? "border-[var(--nav-active-border)] bg-[var(--nav-active-bg)] text-[var(--text)]"
+      : "border-[var(--hairline-soft)] bg-[var(--surface-sunken)] text-[var(--text-muted)] hover:text-[var(--text)]",
+  );
+}