You can't copy it, you can relate both databases and create a rollup from the select property.
That will display in tasks the rollup with the selected items in the project database and using the new formulas will let you call the tags as well.
Keep in mind this is not creating tags in your database, it is just displaying which selection is present in the projects database.
You may need a tags database and that way you can relate projects and tasks as needed.
Other option is to use external tools like Make or Zapier to create an automation that create the tags.