What do you call application modules that are responsible for business logic?

It's not that universal, but we have named a few things "Engines", for example Balancing Engine. We also use services, but they are actually independent programs that performs jobs. Engine are used in other places, such as the ViewModels, or in the services.

We put them in the DomainModel project which most things reference though. That's were most basic functionality and shared resources end up if they are used across Client/Service/Backend projects. So Domain / DomainModel might be a thing to use as well, if you want a specific namespace for that kind of use.

We call that business logic layer “services” at work too, for lack of a better word, but I’ll be watching over this thread for better ideas…

In respect to sitting above the API layer and turning DTO's to/from Domain Object's, I'd call them "Brokers".

Stealing from "Domain Driven Design", I think calling them "domain objects" is appropriate.

We had a separate namespace called BusinessLayer, often abbreviated BL.

i call then the "domain".

At their most general, they are "data processors." In common parlance, they're often called "algorithms," although some folks insist that that is reserved for programs with trivial control flow. For disambiguation and comparison:

• A service is an API surface and a contract promising that the surface has certain behaviors; data processing may be part of how the API is implemented. In practice, a service is e.g. an HTTPS endpoint and an OpenAPI specification.
• A capability is a copyable token which simultaneously authorizes its holder to perform an action and designates the holder as having the authority to perform that action. This won't be part of your normal curriculum and training; see this post for an introduction, or this story for motivation.
• A controller is a modulator for a (distributed) system. Typically a controller is anything which is actuated by a control loop, although sometimes a controller can sit outside of the system. Common examples include MVC patterns, k8s components, and video-game controllers.

Daemons?

Services or uscases

Business services

We call the things that, "sit in the middle," Middleware.

I'm not completely sure which classes you're talking about - but it sounds like the Business Process Layer

I would call them “services” but I’m looking for a less overloaded term. Maybe capabilities? Controllers?

"Controllers" (in dotnet at least) is usually reserved for the class that initially intakes the http request after middleware (auth, modelbinding etc)

It's probably easier with a concrete example, so lets say the action is "Create User"

It depends on the rest of your architecture, but I usually start with a UserController - that takes all user related requests.

To make sure the Controller doesn't get super big with logic, it sends it though mediatr to a CreateUserCommandHandler

But it's a big vague which parts you're asking about..

"there is a class of … classes/modules that does the needful.".

Everything else you've described

"API resources, queue workers, repositories, clients" and serializers

Is "cross-cutting", "Data Access Layer", and "Service Agent Layer" maybe a bit "Anti-corruption Layer" - but there's a lot of other things in between that "do the needful"

I would call them “agents” at a class layer and encapsulate the logic specific to each domain in its own class. Completely arbitrary but in my mind: adapters - call other web services

dao - database calls

agent - responsible for stitching the pieces all together and doing the actual business logic.

Example: OpenWeatherAdapter - call the OpenWeather API. No business logic. H2SelectDao - get user preferences from an internal database. No business logic.

WeatherAgent(openWeatherAdapter, h2SelectDao) - All the business logic.

Note: this is in context of a API service like a middleware.