Make sure iCloud Photos sync is enabled. You'll go to Settings -> Tap on your name on the top -> iCloud -> Photos.
You'd want the setting "Sync this iPhone" to be set ON.
The sync process may take a considerable amount of time. Make sure you're on a good Wifi or Network connection to do this process. Let it sit for several hours and you should see all photos from your Photos app being synced.
One way to test, and see what actually is sync-ed to iCloud is by trying the iCloud web interface. To do this:
Open Safari on your Mac or on any modern browser on your windows machine.
Go to: https://icloud.com
Click on the "Sign in" button.
Log in with your Apple ID (the same you use on your iPhone)
Once logged in, you'll see a "Photos" icon on the main screen (in a box on the bottom left). This will open a web based version of your Photos App in your browser, and you should see all the photos that are sync'ed over to iCloud. This way you can spot if there are any photos missing.