Even Zephyr is multi tenant and works the same as Jira, even though you are seeing the update message individually but when the admin performs the upgrade it will upgrade the Plugin and thus upgrading it for everyone on the instance and not specifically for you. Additionally this is a very important update that needs to be applied as soon as possible so that you can get the latest changes/bug fixes that have been released. Until this process is manually done, this one time, your instance will not be getting any further updates of the Zephyr plugin.
Ideally on the cloud there is no need of a manual update and Zephyr plugins are updated automatically when ever we push an update on our end. In this specific instance its an exception cause of a Jira policy. Couple of months back we have added a SCOPE change to our app so that we can be better aligned with the Jira permissions scheme and provide a more fine grain control on Zephyr functionality with respect to permissions, whenever such a change occurs Jira blocks the automatic updates of apps until this change is manually updated on the instance. The corresponding Jira documentation is available as a "Learn More" link on the update banner.
Once this update is manually done, the auto update of apps resume and your Zephyr plugin will be upto date as and when we push updates.
Please let me know if this answers your/your admins's questions in order to go ahead with a manual update just this once cause of the reason mentioned above.