"The following modules are missing or built with a different engine version" with a new project

When I run the DebugGame Editor configuration is VS (is it what you meant by run the editor in debug mode?), I get the same error, only difference is that the dll name is a little bit different (with -Win64-DebugGame appended).

What do I need to do after switching engine version? Do you mean I need to create the project using 4.10 and then switch it to 4.11 and open it in 4.11?