missing button duplicate Photos

There is no Duplicate button to push, to trigger the scan for duplicates. The scan for Duplicates is fully automatic. Once Photos has finished the scan of your library, you will see a Duplicates album in the sidebar, below the "Imports" album, but only, if Photos could recognise at leat one pair of Duplicates. See: Remove duplicate photos in Photos on Mac – Apple Support (UK)

Richard is right, we need to be patient. For my moderately sized library it took three weeks until the Duplicates album appeared in the sidebar.

The Duplicates folder won't appear until Photos has had time to go through all your picture to find things to put in it. This could take awhile. How long has it been since you updated to Ventura?