Add setting to exclude extensions with disabled auto-update from badge count

[Copilot]

Extensions with automatic updates disabled now often represent the only "outdated" items in the badge, creating notification fatigue when updates are intentionally deferred.

Changes

• New setting: extensions.excludeDisabledAutoUpdateFromBadge (default: false)

  • When enabled, filters extensions without auto-update from the activity bar badge count
  • Badge updates immediately on configuration change via event listener
  • Extensions view continues showing all available updates regardless

• Badge calculation (StatusUpdater.onServiceChange):

  • Checks isAutoUpdateEnabledFor(extension) when setting enabled
  • Maintains existing behavior when disabled (default)

• Configuration key export: ExcludeDisabledAutoUpdateFromBadgeKey constant added for reusability

Default behavior unchanged—all outdated extensions appear in badge unless setting explicitly enabled.

Original prompt

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This section details on the original issue you should resolve

<issue_title>Exclude extensions with auto updates disabled from available updates on badge</issue_title>
<issue_description>

Short description
Introduce a setting to suppress including extensions which have updates available AND automatic updates disabled from the badge on the Extensions icon in the Activity Bar which shows the number of available updates.

Full description
When there are updates available for installed extensions VS Code displays a badge on the Extensions icon in the Activity Bar with the number of extensions with pending updates. Usually this is a helpful visual indicator but it can have the opposite effect for extensions which have had automatic updates disabled. In this scenario, it's common that all extensions are up-to-date except for those that have been deliberately opted-out (i.e. the badge is showing just the number of extensions with automatic updates disabled which have available updates).

This issue is to request the addition of a setting which allows for excluding extensions with automatic updates disabled from the calculation of the number of extensions with pending updates shown as a badge on the Extensions icon. Note this only pertains to the badge; available updates for all extensions, including those with automatic updates disabled, would still be shown as usual when the Extensions pane is focused.

Rationale
A common reason for disabling automatic updates for an extension is due to a serious bug in a newer version which would break important functionality. Another still is that broader changes to the workspace are required before the extension can be updated. In these scenarios, the available updates badge only serves as an annoying distraction as the updates can't (or shouldn't) be performed.</issue_description>

Comments on the Issue (you are @copilot in this section)

• Fixes Exclude extensions with auto updates disabled from available updates on badge #285779

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