Update for future reference.
The issue seems to be caused by opening multiple projects that uses the same language server — in this case, Gopls. The language server’s workspace is defined only once by BBEdit when a project is opened. Each subsequent project inherits the same workspace, which might confuse certain servers.
For instance, if I open BBEdit, then open the Go project "/Developer/foo", the server’s workspace is correctly set to "/Developer/foo", and everything works fine. If I then open another Go project, say "/Developer/bar", without quitting BBEdit, the server still assumes the workspace is "/Developer/foo”.
The issue can be “solved” by closing all projects and reopening BBEdit.
Bare Bones is aware of this limitation, which might be addressed in future version.