Refactor duplication startup publication

[Weidong Cui (wdcui)]

This PR makes broker process startup source-neutral, restricts production creation to a shared process-and-initial-thread path, and prepares duplication children only for parent-death behavior while every runner uses the same association activation path.

[github-actions]

🤖 SemverChecks 🤖 ⚠️ Potential breaking API changes detected ⚠️

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--- failure inherent_method_missing: pub method removed or renamed ---

Description:
A publicly-visible method or associated fn is no longer available under its prior name. It may have been renamed or removed entirely.
        ref: https://doc.rust-lang.org/cargo/reference/semver.html#item-remove
       impl: https://github.com/obi1kenobi/cargo-semver-checks/tree/v0.50.0/src/lints/inherent_method_missing.ron

Failed in:
  BrokerProcess::begin_duplication, previously in file /home/runner/work/litebox/litebox/target/semver-checks/git-ulitebox/e2932b81761b715e3f7f68dbe7c240fea3dc87df/litebox_broker_core/src/process.rs:548
  BrokerProcess::mark_abnormal, previously in file /home/runner/work/litebox/litebox/target/semver-checks/git-ulitebox/e2932b81761b715e3f7f68dbe7c240fea3dc87df/litebox_broker_core/src/process.rs:678
  BrokerCore::create_process, previously in file /home/runner/work/litebox/litebox/target/semver-checks/git-ulitebox/e2932b81761b715e3f7f68dbe7c240fea3dc87df/litebox_broker_core/src/lib.rs:334

--- failure struct_missing: pub struct removed or renamed ---

Description:
A publicly-visible struct cannot be imported by its prior path. A `pub use` may have been removed, or the struct itself may have been renamed or removed entirely.
        ref: https://doc.rust-lang.org/cargo/reference/semver.html#item-remove
       impl: https://github.com/obi1kenobi/cargo-semver-checks/tree/v0.50.0/src/lints/struct_missing.ron

Failed in:
  struct litebox_broker_core::BrokerThread, previously in file /home/runner/work/litebox/litebox/target/semver-checks/git-ulitebox/e2932b81761b715e3f7f68dbe7c240fea3dc87df/litebox_broker_core/src/process.rs:125
  struct litebox_broker_core::DuplicationTransaction, previously in file /home/runner/work/litebox/litebox/target/semver-checks/git-ulitebox/e2932b81761b715e3f7f68dbe7c240fea3dc87df/litebox_broker_core/src/process.rs:222