The script library is present independently in all scopes, but Vision Client Tags are only present in Vision scope.
The designer tree has to have something selected under Vision for the tag browser to show Vision Client Tags.
The workaround is to float your project library script windows then pick a Vision item in the tree. Your tag browser will then include Vision Client Tags while your project library scripts remain editable. (Right click on the script's tab at the bottom of the editor to find the float option.)