Firstly, the error has nothing to do with "Copy Local" being True or False.
So, you have a separate DLL project that contains your CustomComboBox as Win Form UserControl, right? It looks like, this project has references to AutoCAD .NET assemblies, or at least the reference of AcdbMgd.dll.
So, which copy of the AcdbMgd.dll is referenced in this project? The copy in the AutoCAD install folder (i.e. the one comes with AutoCAD installation)? or the one downloaded from ObjectARX SDK download/Autodesk's Nuget package? For development, especially when you need to refer to AutoCAD .NET API in UI development, you cannot use the AutoCAD .NET references coming from AutoCAD installation, because when Visual Studio loads the custom UI in its designer, it has to load the referenced AutoCAD .NET DLL. Since the AutoCAD .NET DLL can only be loaded with AutoCAD runtime (meaning inside AutoCAD process), hence the error you saw. On the other hand, the AutoCAD .NET DLLs from the ObjectARX SDK/Nuget package is a strip-down version with the dependencies to AutoCAD runtime being removed as much as possible, so VS designer can load it (in order to get all the interfaces - properties/methods - covered by the .NET API). If you look at the file size of Acdbmgd.dll: ~2Mb from SDK/Nuget, ~6MB from AutoCAD installation. The one from SDK/Nuget is only for development, and cannot be used for running your code. That is why you MUST make sure "COPY Local" to be False.
Also, even you use the DLLs from SDK/Nuget, it is no guarantee, I guess, the same error will never happen.
Now that you go all the way to have a separate project for your custom UI components, which is a good base step of making the better code/component reusability, you might want to go one step further to separate UI with business data (AutoCAD data in this case), so that the UI component (the CustomComboBox, in your case) does not refer to any AutoCAD API data. You can search for suitable UI design patterns for this, but the most common pattern for Windows desktop app is to use WPF with MVVM pattern, with which you can easily avoid the error you ran into.