Calendar Search not working on iPhone 13

Assuming you are having problems with your iCloud account calendar:

Settings > Calendar > Accounts (select the account of the calendar you are having issues searching) > iCloud > Apps Using iCloud select Show All > Select iCloud Calendar > Toggle off Use on This iPhone > Select Delete from my iPhone > Wait 1 minute then toggle back on. Calendars will come back from your iCloud. Give it some time and the search will begin working again.

(Sorry this might sound dumb) Have you tried searching for an event you know you have put in the calendar?

If so, is that calendar enabled? (Bottom bar > Calendars > If there is a check by that calendar then it is enabled)

Is the search button not appearing or is it not searching your events?