Add auto-update feature for basic-memory

[groksrc]

Description

Basic Memory should support automatic updates, enabled by default, so users stay on the latest version without manual intervention.

This is especially important given that:

• The cloud server may be running a newer version than the client
• API response schema changes (API response schema breaking changes break released clients #638) can silently break older clients
• Config format migrations (Config migration does not preserve backup of old format #637) can create incompatibilities between versions
• Users may not realize they're running an outdated version until things break

Proposed Behavior

• Enabled by default — users should get updates automatically unless they opt out
• Check for new versions periodically (e.g., on startup or daily)
• For homebrew installations: trigger brew upgrade basic-memory
• For pip/uv installations: notify or auto-upgrade via uv pip install --upgrade basic-memory
• Add a config option to disable: "auto_update": false
• Show a notification when an update is available if auto-update is disabled

Config Example

{
  "auto_update": true,
  "update_check_interval": 86400
}

Related Issues

• Config migration does not preserve backup of old format #637 — Config migration breaks older versions (auto-update would prevent version skew)
• API response schema breaking changes break released clients #638 — API schema changes break released clients (auto-update keeps clients compatible)

[claude]

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