I searched the PHPStorm documentation on JetBrains to use the setup of the same deployment server in multiple projects.
Open the deployment window via Menu:
Tools -> Deployment -> Configuration
There is a flag in the configuration window “Deployment” for each entry you created in the top of the tab “Connection” named with “Visible only for this project“. Disable this flag for each entry you decide using this in another projects and you will be happy to use this setting in other projects.