fix(paths): one home-prefix helper, so labels abbreviate on both platforms

The rule "show ~/project rather than /home/<user>/project" had three
implementations in the frontend, two of them platform-specific in opposite
directions, so each looked correct to whoever wrote it.

- The Run menu's Recent Sessions rows matched /home/<user>/ only. On macOS
  nothing was stripped, so every row spent its first ~19 characters on an
  identical /Users/<user>/ prefix and the left-to-right ellipsis removed the
  tail that identifies the row. That is #273, reported by @jordan8037310, who
  also traced why the menu's 250px cap made it worse: the width was chosen on
  the assumption the abbreviation had run.
- The case-manage list matched /Users/<user> only, the mirror image, so on a
  Linux host no case path was ever abbreviated there. Unreported.

Both now call _shortenHomePath(), which was already correct for both layouts
and already used by the Resume list, Cmd+K, the desktop home rail and the phone
overview. Its regex collapses to one alternation with a lookahead, so a path
that is exactly $HOME renders "~" instead of being left raw, matching what the
case-manage list used to do on macOS.

test/home-path-abbreviation.test.ts pins the helper on both layouts and the
rendered case-manage label, and fails if a fourth copy of the pattern appears in
src/web/public. The Run-menu guard counts helper calls rather than pinning a
source line, so it survives the row restructure in #274.

test/run-mode-ui.test.ts gains a _shortenHomePath stub: its harness loads
session-ui.js without terminal-ui.js, which the real app never does.

Verified against an isolated instance with 27 real cases and 50 history rows:
27 of 27 case paths and 17 of 20 Run menu rows abbreviate, the other 3 are
/tmp paths that correctly stay raw, tooltips keep the full path, no page errors.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

src/web/public/session-ui.js

@@ -489,7 +489,11 @@ Object.assign(CodemanApp.prototype, {
         const date = new Date(s.lastModified);
         const timeStr = date.toLocaleDateString('en', { month: 'short', day: 'numeric' })
           + ' ' + date.toLocaleTimeString('en', { hour: '2-digit', minute: '2-digit', hour12: false });
-        const shortDir = s.workingDir.replace(/^\/home\/[^/]+\//, '~/');
+        // Shared helper, not a local regex: the copy that used to live here
+        // matched `/home/<user>/` only, so on macOS every row rendered the same
+        // unabbreviated `/Users/<user>/…` prefix and ellipsized away the tail
+        // that identifies it (#273).
+        const shortDir = this._shortenHomePath(s.workingDir);
 
         const btn = document.createElement('button');
         btn.className = 'run-mode-option';
@@ -2676,7 +2680,9 @@ Object.assign(CodemanApp.prototype, {
     cases.forEach((c, idx) => {
       const isFirst = idx === 0;
       const isLast = idx === cases.length - 1;
-      const pathDisplay = c.path ? c.path.replace(/^\/Users\/[^/]+/, '~') : '';
+      // Was `/Users/<user>` only, the mirror image of the Run menu's bug: every
+      // case path on a Linux host rendered in full, unabbreviated.
+      const pathDisplay = c.path ? this._shortenHomePath(c.path) : '';
       html += `
         <div class="case-manage-item" data-case="${escapeHtml(c.name)}">
           <div class="case-manage-info">

src/web/public/terminal-ui.js

@@ -1610,11 +1610,21 @@ Object.assign(CodemanApp.prototype, {
     return workingDir.split('/').pop() || workingDir;
   },
 
-  /** Normalize home prefixes to "~/" on both Linux and macOS */
+  /**
+   * Normalize a home prefix to "~" on both Linux (`/home/<user>`) and macOS
+   * (`/Users/<user>`). The lookahead lets the home directory ITSELF match, so a
+   * path that is exactly `$HOME` renders "~" instead of being left raw.
+   *
+   * This is the only place that pattern belongs. Two hand-rolled copies had
+   * drifted, each broken on the platform its author was not using: the Run
+   * menu's matched `/home/` only, so on macOS nothing was stripped and every
+   * Recent Sessions row spent its first ~19 characters on an identical
+   * `/Users/<user>/` prefix (#273); the case-manage list's matched `/Users/`
+   * only, so no Linux path was ever abbreviated there. Route new path labels
+   * through here rather than writing a third copy.
+   */
   _shortenHomePath(p) {
-    return (p || '')
-      .replace(/^\/home\/[^/]+\//, '~/')
-      .replace(/^\/Users\/[^/]+\//, '~/');
+    return (p || '').replace(/^\/(?:home|Users)\/[^/]+(?=\/|$)/, '~');
   },
 
   /**