Yes, you did the right thing!
My apologies for not mentioning this sooner, but as you noticed templates and vocabularies are not stored in your project file but elsewhere in your local Tropy ‘installation’ – this is because you might want to share templates across different projects. Therefore, if you work on the same project on different devices you should also install the templates you use on both of them. Hopefully templates won’t change frequently so that it is not too much work to keep them in sync (you could make it a habit to export the template after every change and keep it next to your project file on OneDrive). We’re currently working to set up a central template repository with which Tropy can sync its templates, so sharing templates will become easier in the future.