"Auto-update failed" banner persists despite healthy install already on latest version; /doctor does not reconcile it

Environment

• Claude Code 2.1.168
• Native installer (~/.local/share/claude/versions/, symlinked from ~/.local/bin/claude)
• macOS arm64, Darwin 25.4

Symptom

The status line shows Auto-update failed · Run /doctor. Running /doctor reports nothing about auto-update (in my case it only flagged an unrelated MCP server timeout). The banner persists and /doctor does not clear or explain it.

Evidence the install is actually healthy

• claude update → Claude Code is up to date (2.1.168), exit code 0
• ~/.local/share/claude/versions/ and ~/.local/bin are writable
• 1.6 TiB free disk
• No lock/staging leftovers under ~/.local/share/claude/
• The versions dir mtime shows a background update attempt did run (~08:05) and failed transiently, but the resulting state is correct (already on the latest version)

Expected

A transient background auto-update failure should not leave a sticky "Auto-update failed" banner once a subsequent check confirms the install is current. /doctor should either clear the stale banner or explain what is actually wrong.

Actual

The banner stays after the failed background attempt; claude update succeeds and reports up-to-date; /doctor neither explains nor fixes the banner.

Repro (approximate)

1. Be on the latest version via the native installer.
2. Have a background auto-update attempt fail transiently (e.g. brief network/registry hiccup).
3. Observe the persistent Auto-update failed · Run /doctor banner.
4. Run /doctor — it does not address the auto-update banner.
5. Run claude update — reports up-to-date, exit 0, but the banner remains.