search function on icloud calendar

There is no option for serching calendar events in iCloud.com , however the calendar events can be searched from the calendar application that is synced ( in Mac system preferences > iCloud , the box of calendar is checked ) see the articles

https://support.apple.com/en-in/guide/calendar/search-for-events-in-calendar-on-mac-icl2cc2c76a7/mac

https://support.apple.com/en-in/guide/calendar/icl1010/mac

https://support.apple.com/en-in/guide/mac-help/narrow-search-results-mh15155/mac

You can send your feedback https://www.apple.com/feedback/icloud.html

https://www.apple.com/feedback/calendar.html

iCloud synched to your iPhone calendar allows searching but not on a non-MAC desktop. iCloud calendar is not a great option and I will go back to MS Office to use the calendar and email which is much more user friendly.

There are left and right arrows in month view , if you click on left arrow but that has to be clicked multiple times to view last year month and its event , the spotlight search is not an feature in iCloud.com