Calendar

It is not possible to search back more than one year. However, if you go to the Month view, you can scroll back and see more than one year. That has always been a setback of the calendar. You can provide feedback to let Apple know you would like to see that here, Feedback - iPhone - Apple

There are a number of 3rd party calendar apps that are much better than Apple’s, and that can search any date range. This is consistent with Apple’s approach of keeping built in apps basic, so it gives more opportunities for developers to produce more robust apps. The one I use is Week Calendar, which has carried forward from Palm Pilot days and even before that from the HP 95/100/200 PDAs. My calendar goes back to 1998, and I can search back that far. It has a lot of features beyond just search; it can sync settings across devices, has “templates” for frequently inserted events, groups of events that can be inserted as one, icons for events and a lot more.

But there are also many other excellent calendar apps; I just continue to use Week Calendar out of 20+ years of habit.