Rename RegisterHandler to AddHandler in Disposable Funcs API

[Copilot]

Pure naming refactor across the Disposable Funcs API surface. No behavior, signature, or disposal semantics changes.

• Interface: IFuncSubscriber.RegisterHandler → AddHandler (all overloads)
• Abstract base: AbstractFuncSubscriber.RegisterHandler → AddHandler
• Implementations: FuncCore, DisposableFunc, FirstFunc
• Extensions: FuncSubscriberExtensions, VoidFuncExtensions
• Call sites: Benchmarks, tests
• XML docs: Updated "registration" → "addition" wording

// Before
func.RegisterHandler(x => FuncResult<int>.From(x * 2));

// After
func.AddHandler(x => FuncResult<int>.From(x * 2));

Repo-wide search confirms zero remaining occurrences of RegisterHandler. All 353 tests pass.

Original prompt

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This section details on the original issue you should resolve

<issue_title>Refactor: Replace RegisterHandler with AddHandler in Disposable Funcs</issue_title>
<issue_description># Refactor: Replace RegisterHandler with AddHandler in Disposable Funcs

Goal

Standardize the API naming in Disposable Funcs by renaming and updating all references from RegisterHandler to AddHandler.

This is a pure naming refactor:

• No behavior changes
• No disposal/lifecycle changes
• No signature redesign (other than the method name)

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Scope

Apply to all places in the repository, including:

• Public APIs
• Interfaces
• Implementations
• Extension methods
• Internal call sites
• XML documentation
• Unit tests
• READMEs / docs / examples
• Comments (where it refers to the method)

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Required Changes

1) Rename the method

Rename every RegisterHandler(...) method in the Disposable Funcs API surface to AddHandler(...).

Before

• RegisterHandler(...)

After

• AddHandler(...)

Keep everything else identical:

• Parameters (names/types/defaults)
• Return type
• Nullability annotations
• Generic constraints
• Overloads

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2) Update interfaces + implementations

If any interface exposes RegisterHandler, rename it to AddHandler and update all implementations.

Example shape (do not introduce this exact interface unless it already exists):

• IDisposable AddHandler(Action<T> handler);

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3) Update all call sites

Replace all usages of:

• someDisposableFunc.RegisterHandler(...)

With:

• someDisposableFunc.AddHandler(...)

Prefer IDE rename / symbol rename to avoid missing references.

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4) Update XML docs + comments

Update all documentation strings to match the new term.

Replace wording such as:

• “Registers a handler …”
  With:
• “Adds a handler …”

Also update any <seealso> or references that mention RegisterHandler.

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5) Update tests

• Rename test method names containing RegisterHandler
• Update test code to call AddHandler
• Ensure all tests compile and pass
• If any tests use reflection over method names, update those strings

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6) Repo-wide search & cleanup

Ensure zero remaining occurrences of RegisterHandler by searching the repo:

• Source
• Tests
• Docs
• Examples
• Comments

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Non-Goals

• Do not change runtime behavior
• Do not change performance
• Do not change disposal semantics
• Do not change handler invocation order or timing
• Do not rename unrelated APIs

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Acceptance Criteria

• All RegisterHandler method declarations in Disposable Funcs are renamed to AddHandler
• All interface members updated and implementations compile
• All call sites updated
• All XML docs / docs / examples updated
• Repo search for RegisterHandler returns no matches
• All unit tests pass
• CI passes</issue_description>

Comments on the Issue (you are @copilot in this section)

• Fixes Refactor: Replace RegisterHandler with AddHandler in Disposable Funcs #39

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