If you are using an institutional Office365 subscription (enterprise, educational, etc.), you are not asked for license keys. Your organization’s login credentials are used, which are validated against the list of users supplied by your organization. This sounds like the way you activated your copy.
It’s not a problem, but your license will expire if you should leave the organization - at which point, you’ll need to sign out from your organization’s account and sign in to a personal Microsoft ID and pay for your own subscription (or provide a license key if you have a perpetual license.)
As for auto-save, as far as I know, auto-save only works for documents that are stored on a Microsoft cloud server (e.g. OneDrive or SharePoint). I have never seen a modern version of office auto-save to local storage.
As for UI changes, that’s the nature of an Office365 subscription. You will always have the latest version (or the latest that your organization has authorized), but that also means there is no way to go back to older versions.
It appears that your organization has not authorized your account to get the latest version (or maybe you just haven’t run auto-update yet). My installation Excel365 is version 16.47.21032301 (which I assume means a March 21, 2021 release). Other Office365 apps are slightly older, at version 16.47.21031401 (which I assume is March 14).