Replace RecursiveApply functions with AutoBroadcaster wrappers

[dennisYatunin]

Purpose

This replaces the RecursiveApply module with a new interface that follows the opposite design pattern: instead of defining functions for Tuples and NamedTuples that need to be called in Fields, Operators, MatrixFields, and external libraries like ClimaAtmos, we can now use a wrapper for Tuples and NamedTuples that behaves the same way when passed to standard math functions. The number of places where this interface needs to be explicitly used is quite small, making it possible to decouple iteration over field variables from most of ClimaCore's internals.

Content

• Introduce the AutoBroadcaster wrapper, which triggers nested_broadcast (an analogue of the old RecursiveApply.rmap) when passed to any common math function or constructor
  • Replace all RecursiveApply functions in ClimaCore's source code with standard math operations
  • Make it possible to add support for any iterator type T by defining the method is_auto_broadcastable(::T) = true, as long as T is compatible with UnrolledUtilities
• Preserve backward-compatibility with original RecursiveApply implementation
  • Add a RecursiveApply module that defines the same functions as the old version, but as simple wrappers around add_auto_broadcasters and drop_auto_broadcasters
  • Define an auto_broadcasted function that automatically introduces calls to either add_auto_broadcasters or drop_auto_broadcasters in Broadcasted expressions, allowing ClimaCore operators to be used in the same expressions as user-defined functions that are incompatible with AutoBroadcasters (e.g., functions that dispatch on non-AutoBroadcaster types)
• Unify broadcasting across DataLayouts, Fields, and Operators
  • The broadcastable form of any AbstractData or Field has add_auto_broadcasters applied to its values
  • Calling Base.broadcasted triggersauto_broadcasted instead of the standard Broadcasted constructor
  • The result of eltype is the output of unsafe_eltype, which acts as an unrolled version of Base.Broadcast.combine_eltypes
  • The result of similar uses the output of safe_eltype, which can identify the first point during inference where a non-concrete type appears in a broadcast expression (essentially a simplified and corrected version of the old call_with_first)
• Update the implementation of new to avoid segfaults and other errors when dealing with DataType fields
• Refactor the deformation_flow.jl example by removing all loops over field variables, adding several missing cases, and clarifying precisely what needs to be tested

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• Code follows the style guidelines OR N/A.
• Unit tests are included OR N/A.
• Code is exercised in an integration test OR N/A.
• Documentation has been added/updated OR N/A.

[nefrathenrici]

This looks good to me. It's nice to get rid of RecursiveApply. I didn't have any significant comments.

[imreddyTeja]

I left some comments and questions, but this looks mostly good to me