Currently, after you deploy a validated package it no longer appears under the Validated Packages menu, however, if you still have the link for the validated package and navigate to that package it doesn't give you any indication that the package has already been deployed and allows the user to click the Deploy button again, assuming they have deploy permissions on the target org connection.

As part of our production deployment approval process, we store the link to the validated package in our external ticketing system (https://app.gearset.com/validated-package-details?deployPackageId=<package id here>). When completing the ticket, users use that link to navigate to the package and complete the deployment. If multiple users happen to click on the link, you cannot tell if it's already been deployed. It seems like that page should prevent you from deploying the same validated package again, given that you can no longer access that validated package from the normal menu.