When the rule gets compiled, the GetFunctionSet classmethod of Ens.Rule.Utils enumerates all classmethods of Ens.Rule.FunctionSet and of all its subclasses in the namespace. The first occurrence of a classmethod name is recorded, and the class in which it's found is going to be the one that the compiler uses when it generates the rule's class code.

In your case SendToEaling is first found in LNWDeploy.RoutingRules.Utility rather than in LNWTIEPackage.RoutingRules.Utility (which collates later).

Per your comment, I think you'll need to specify the full reference to your function, i.e.

##class(LNWTIEPackage.RoutingRules.Utility).SendToEaling(HL7)

Update: so far I haven't found a way of explicitly indicating which class you want your custom utility function to be called in.

I'm not clear what Tomcat has to do with your attempts to use Atelier. Atelier connects to Cache / Ensemble / HealthShare / IRIS servers, typically via the same webserver you use when managing those servers through InterSystems' Management Portal. This could be the private Apache instance that InterSystems installs by default, and which by default runs on port 57772.

Did you consider creating a Studio Project containing everything you need? Then you can export the project to XML in a way that includes all the members of the project as well as the project definition.

It's also worth knowing that if you go to the Namespace tab of the Workspace pane, then expand Classes, you can right-click on a package and add the package to your current project. This may be better that adding individual classes to your project, because by adding the package you ensure that any classes added later to the package will be exported too.