VS Code isn't actually that bad with its extension and application updates. When an extension has been updated, it'll try to load the new version in-memory (if the extension supports it), otherwise it'll add a badge to the Extensions panel icon in the sidebar, leaving a subtle reminder that you need to restart in order to get the new extension update. For updates to VS Code proper, it adds a badge to the settings icon. No popups or notifications. You can also disable auto-updating for extensions and the application if you find the badges distracting.

Now, if certain extensions try to get your attention with notifications or automatically opening release notes, that can absolutely be a problem. Extensions vary wildly in quality, since the barrier for publishing one is effectively nothing. These leaves the job of curating good, non-spammy extensions up to the developer.