Managed && !"@Singleton"

(I'm omitting the fully-qualified class name for brevity)

If I also wanted to look for HealthCheck classes I could update the query to:

(Managed || HealthCheck) && !"@Singleton"

I think it also helps that OpenGrok has a separate input for filtering file paths (completely splitting the "where" and the "what" parts of the query). And this file path search supports the same boolean operators. So if I want to narrow my search to two particular repositories I could put CrmSearch || AutomationPlatform into the File Path input. And because this input only handles file paths, I don't need to remember any special syntax. Whereas if you clump the entire query into a single input, then users need a way to tell you whether a search term applies to file paths or file contents.