Custom Type Search/Filter

The number of Custom Types in my project is getting a quite large. When adding a property to an object, the interface for picking the property to add is a simple dropdown and a text field for naming it. The dropdown is in alphabetical order, which does help a bit, but it would be nice if I could search/filter these properties by name.

**Describe the solution you'd like**
Ideally, a bit more UI in the "Add Property" dialogue would be great. Something like a scroll box instead of a dropdown, with a search field at the top to filter what I'm looking for.

**Describe alternatives you've considered**
I don't think there are any alternatives to this at the moment. Maybe I could make my own plugin that has the UI I'm looking for, but I haven't looked into if that's possible.

No files, tests, or entry points are named. Start by locating the Add Property dialog and its custom-type selection control, then trace how available types are populated; done means the dialog provides a name-based search or filter and shows only matching custom types.

Written by the indexing model from the issue text.