Describe the bug

On the network plugin screen, 2 update messages appear for plugins which have an update available.

From VIP Support

We have potentially identified the source of the duplication. We do not rely on core's notice since users cannot update plugins from the plugin dashboard but we add the notification manually here:

https://github.com/Automattic/vip-go-mu-plugins/blob/develop/codebase-manager/plugins/plugins-manager.php#L17

And at the same time it seems like 10up is doing the same here:
https://github.com/wpcomvip/gus-wp/blob/trunk-built/plugins/10up-experience/includes/classes/Plugins/Plugins.php#L181

Steps to Reproduce

n/a

Screenshots, screen recording, code snippet

Environment information

No response

WordPress information

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