As you correctly summarized, there currently are two ways to search in Apex Designer. The one in the toolbar searches all the generated files in the project. As an aside, it can also search across all the projects (apps and libraries) that you have access to.
The second one is the search icon button on the User Interface page. This searches all the user provided content in that user interface (including methods).
Your suggestion for a kind of “metadata search” is a good one. Perhaps it could present the results similar to the branch status page.
For now, if you are trying to find something in a method of a user interface or a behavior on a business object, you can try a few tricks. If you are looking for references to a property name “weight”, try searching for “.weight”. That will filter out the numerous references to the property in model files, etc. If you get a hit in a TypeScript (.ts) file, you can click the Next Occurrence to jump to it and then scroll up to see what method or behavior it is contained in.
Hope that helps.
