Refactor duplicated code in resiliency examples and channel classes

[Copilot]

Identified and eliminated ~134 lines of duplicated code across resiliency examples and channel classes.

Changes

Resiliency Examples

• Extracted common test helpers (universal_ans, validate, mark_faulty_nodes) to libs/full/resiliency_distributed/examples/common.hpp
• Both async_replicate_distributed.cpp and async_replay_distributed.cpp now use shared implementations
• Removed ~90 lines of duplicated code

Channel Classes

• Introduced channel_close_mixin<Derived, T> CRTP base class for shared close() implementations
• Applied to channel<T> and send_channel<T> classes
• Removed 44 lines of duplicated code while maintaining binary compatibility

namespace detail {
    template <typename Derived, typename T>
    class channel_close_mixin {
        // Four close() overloads for different launch policies
        void close(launch::apply_policy, bool force_delete_entries = false);
        hpx::future<std::size_t> close(launch::async_policy, bool force_delete_entries = false);
        std::size_t close(launch::sync_policy, bool force_delete_entries = false);
        std::size_t close(bool force_delete_entries = false);
    };
}

template <typename T>
class channel : public client_base<...>, public detail::channel_close_mixin<channel<T>, T> {
    // close() methods now inherited from mixin
};

All public APIs remain unchanged.

Original prompt

Find and refactor duplicated code

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