fix(dashboard): close 7 review findings on extended-status hardening

Settings inheritance (high):
  - Restored the value !== initialProjectValue gate on the non-model
    project branch. Previously every effective/inherited project key was
    persisted as an explicit override on every save.

Git Manager UI lie in remote-only mode:
  - "Local <branch> vs origin" card now renders "no local tracking"
    instead of a green "Synced" badge when integrationTipSource ===
    "remote-only" (no local branch to compare).
  - New dedicated "HEAD vs origin/<branch>" card surfaces a meaningful
    distance in remote-only mode.

isIndexStale correctness:
  - Walks up to 16 reflog entries so multi-hop misses (A→B→C without
    sync) are detected; the prior check only consulted @{1}.
  - Gated on isOnIntegrationBranch === true so a feature-branch worktree
    whose HEAD happens to descend from <integration>@{1} no longer trips
    the FN-INDEX-DESYNC warning.

Enumeration-failed events surfaced:
  - collectRecentMergeAdvances pairs events with (taskId, newSha) when
    both are present, falls back to taskId-only for early-failure events
    (e.g. "enumeration-failed") that have neither path nor newSha. The
    diagnostic outcome now surfaces on the matching advance instead of
    being silently dropped.

aheadOfIntegration semantics no longer shift:
  - Split into three distinct fields: aheadOfIntegration (HEAD vs local),
    aheadOfIntegrationRemote (HEAD vs origin/<branch>),
    aheadOfOriginIntegration (local vs origin). Consumers no longer have
    to read integrationTipSource to know which comparison they got.

currentBranch failure no longer masks wrong-branch state:
  - Distinguish "command threw" (transient git error) from "command
    succeeded with empty stdout" (legitimate detached HEAD). New
    currentBranchDetectionFailed field lets the UI surface "branch
    detection unavailable" on a real failure.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

packages/dashboard/app/api/legacy.ts

@@ -2583,14 +2583,27 @@ export interface GitStatus {
   integrationBranch?: string;
   integrationBranchSource?: "settings" | "origin-head" | "fallback";
   isOnIntegrationBranch?: boolean;
+  /** True when `git branch --show-current` failed (transient git error,
+   *  permission, etc.). Distinct from detached HEAD (command succeeds with
+   *  empty stdout). UI surfaces "branch detection unavailable" rather than
+   *  silently hiding the wrong-branch warning. */
+  currentBranchDetectionFailed?: boolean;
   integrationTipSha?: string | null;
   /** "local" = `refs/heads/<branch>` exists; "remote-only" = only
    *  `refs/remotes/origin/<branch>` exists and was used as fallback;
    *  "missing" = neither ref exists. */
   integrationTipSource?: "local" | "remote-only" | "missing";
   originIntegrationTipSha?: string | null;
+  /** HEAD vs the **local** integration tip. Undefined when the branch
+   *  exists only as a remote-tracking ref. */
   aheadOfIntegration?: number;
   behindIntegration?: number;
+  /** HEAD vs `origin/<integrationBranch>`. Defined whenever the remote
+   *  tracking ref exists, regardless of whether the local ref does. */
+  aheadOfIntegrationRemote?: number;
+  behindIntegrationRemote?: number;
+  /** Local integration tip vs `origin/<integrationBranch>`. Defined only
+   *  when both refs exist. */
   aheadOfOriginIntegration?: number;
   behindOriginIntegration?: number;
   dirtyDetails?: {