sync: initialize auto-sync after native metered detection

[Dmitriy Vasyura (dmitrivMS)]

Stack

Stacked directly on #331897 (dev/dmitriv/use-vscode-metered). This PR contains only the Settings Sync portion of the original combined change and does not depend on the other consumer PRs. Merge the primary PR first, then retarget this PR to main.

Changes

• Re-evaluate automatic Settings Sync after native metered initialization when startup begins with a conservative metered state.
• Handle an initial unmetered IPC snapshot without relying on a change event.
• Avoid initializing automatic sync after the service has been disposed.
• Update the test client for the metered service readiness contract.

Existing metered suppression and manual sync behavior otherwise remain unchanged.

Validation

• 22 Settings Sync tests passed.
• Client type-check, targeted transpilation, and staged-file hygiene/ESLint passed.
• The diff is limited to two Settings Sync files. Applying all four disjoint sibling diffs to the primary branch exactly reconstructs the original combined PR tree.