Using Outlook for iOS for personal email and calendar management
AFAIK, your iPhone 13 should continue to run Outlook and synchronize your Outlook data normally through iOS 27. The iPhone 13 is supported by iOS 27, and Microsoft’s current policy is that Outlook for iOS supports the two most recent major versions of iOS. So, when iOS 27 arrives, your iPhone 13 should be running a supported iOS version and Outlook should continue to receive updates and synchronize your Mail, Contacts, Calendar and Tasks.
Your automatic updates are helpful here. The iOS 26.2 update you just received does not indicate that your iPhone 13 is approaching an Outlook compatibility problem. It is simply part of Apple's normal update cycle leading into iOS 27. Assuming you continue allowing both iOS and Outlook to update automatically, there is nothing you need to change now.
The longer-term issue is iOS 28. The iPhone 13 was released in 2021 and there is a possibility that iOS 28 could eventually leave the iPhone 13 behind. If that happens, the situation becomes similar to what happened with your iPhone 8, but not right away, because of the reason is Microsoft's two-version Outlook policy. When Microsoft eventually moves Outlook's supported versions forward, an iPhone that is permanently stuck on an older iOS version can eventually fall outside Outlook's supported configuration. Note that an older version of Outlook can continue functioning after it is no longer supported but Microsoft could eventually require a newer iOS version.
Most importantly, you shouldn't have to buy a new iPhone now as a precaution. Your iPhone 13 should satisfy your Outlook requirements. Instead, you might want to would periodically verify after major iOS and Outlook updates that changes made on the iPhone are appearing in Outlook on your computers, and vice versa.
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hth
Marcin