[FEATURE] Claude Desktop on Linux: add an update check (it has no updater at all)

Claude Desktop on Linux has no way to update itself and no way to tell you an update exists. There is no "Check for updates" menu item and no background updater. On macOS and Windows the app updates itself; on Linux the only path is the system package manager.

Why it matters

Desktop bundles its own Claude Code, pinned to a version when the app is built. A new model that needs a newer Claude Code shows greyed out in the Code tab's model picker until the app itself is replaced. On macOS and Windows that happens automatically within a day or two. On Linux it waits on whoever packages the app for the distribution.

It happened on September 22, 2026: the Arch-based distribution's repo carried Desktop 2.2553.1, which bundles Claude Code 2.1.275. Opus 5.5 was greyed out in Desktop while the standalone CLI (2.1.280) on the same machine ran it. Anthropic's own apt repository already had 2.2553.13, which bundles 2.1.280 and fixes it, but nothing in the app said so. Working that out took an hour. The documented-looking escape hatch, CLAUDE_CODE_LOCAL_BINARY, does nothing (#84371).

Request, any of these would have prevented it:

1. A "Check for updates" item that compares the running version with the newest in downloads.claude.ai/claude-desktop/apt and says a newer version exists, even if installing stays with the package manager.
2. A notice when a model is unavailable because the bundled Claude Code is too old ("requires a newer Claude Desktop, you have X, Y is available").
3. Letting Desktop on Linux fetch a newer Claude Code on its own, independent of the app package.

Environment

• Claude Desktop 2.2553.1 (Linux x86_64), later 2.2553.13
• Installed from a distribution repo that repackages Anthropic's .deb
• Related: #84371 (CLAUDE_CODE_LOCAL_BINARY override is read and discarded)