feat(mac): auto-update checker and Plan pane button cleanup

Remove the broken "Connect Claude" / "Reconnect Claude" buttons from
the Plan pane -- they opened a terminal session that did nothing useful
for already-logged-in users. Keep only the "Retry" button.

Add an auto-update checker that queries GitHub releases every 2 days in
the background. When a newer menubar build is available, an "Update"
pill appears in the header. Clicking it runs the existing installer
flow (download, replace, relaunch) with no manual steps.

mac/Sources/CodeBurnMenubar/Data/UpdateChecker.swift

@@ -0,0 +1,87 @@
+import Foundation
+import Observation
+
+private let releasesAPI = "https://api.github.com/repos/getagentseal/codeburn/releases/latest"
+private let checkIntervalSeconds: TimeInterval = 2 * 24 * 60 * 60
+private let lastCheckKey = "UpdateChecker.lastCheckDate"
+private let cachedVersionKey = "UpdateChecker.latestVersion"
+
+@MainActor
+@Observable
+final class UpdateChecker {
+    var latestVersion: String?
+    var isUpdating = false
+    var updateError: String?
+
+    var updateAvailable: Bool {
+        guard let latest = latestVersion else { return false }
+        let current = currentVersion
+        return !current.isEmpty && current != "dev" && latest != current
+    }
+
+    var currentVersion: String {
+        Bundle.main.infoDictionary?["CFBundleShortVersionString"] as? String ?? ""
+    }
+
+    func checkIfNeeded() async {
+        let lastCheck = UserDefaults.standard.double(forKey: lastCheckKey)
+        let now = Date().timeIntervalSince1970
+        if now - lastCheck < checkIntervalSeconds {
+            latestVersion = UserDefaults.standard.string(forKey: cachedVersionKey)
+            return
+        }
+        await check()
+    }
+
+    func check() async {
+        guard let url = URL(string: releasesAPI) else { return }
+        var request = URLRequest(url: url)
+        request.setValue("codeburn-menubar-updater", forHTTPHeaderField: "User-Agent")
+        request.setValue("application/vnd.github+json", forHTTPHeaderField: "Accept")
+
+        do {
+            let (data, _) = try await URLSession.shared.data(for: request)
+            let release = try JSONDecoder().decode(GitHubRelease.self, from: data)
+            guard let asset = release.assets.first(where: {
+                $0.name.hasPrefix("CodeBurnMenubar-") && $0.name.hasSuffix(".zip")
+            }) else { return }
+
+            let version = asset.name
+                .replacingOccurrences(of: "CodeBurnMenubar-", with: "")
+                .replacingOccurrences(of: ".zip", with: "")
+
+            latestVersion = version
+            UserDefaults.standard.set(Date().timeIntervalSince1970, forKey: lastCheckKey)
+            UserDefaults.standard.set(version, forKey: cachedVersionKey)
+        } catch {
+            NSLog("CodeBurn: update check failed: \(error)")
+        }
+    }
+
+    func performUpdate() {
+        isUpdating = true
+        updateError = nil
+
+        let process = CodeburnCLI.makeProcess(subcommand: ["menubar", "--force"])
+        process.standardOutput = FileHandle.nullDevice
+        process.standardError = FileHandle.nullDevice
+
+        do {
+            try process.run()
+        } catch {
+            isUpdating = false
+            updateError = error.localizedDescription
+            NSLog("CodeBurn: update spawn failed: \(error)")
+        }
+    }
+}
+
+private struct GitHubRelease: Decodable {
+    let tag_name: String
+    let assets: [GitHubAsset]
+}
+
+private struct GitHubAsset: Decodable {
+    let name: String
+    let browser_download_url: String
+}