icloud calendar

See the article https://support.apple.com/en-in/guide/iphone/iphdafdf98a1/ios

Keep your Calendar up to date across your devices

You can use iCloud to keep your Calendar information up to date on all your devices where you’re signed in with the same Apple ID.

Go to Settings  > [your name] > iCloud, then turn on Calendar.

If you don’t want to use iCloud for your Calendar, you can sync your Calendar information between your iPhone and your computer. See Sync iPhone with your computer.

Read https://support.apple.com/en-in/guide/iphone/iph3d110f84/ios

If you add an appointment to the calendar via iCloud.com on a computer browser does it show on the iPhone? Trying to identify whether the iPhone is the problem here or not.