Fix side conversation config inheritance

[etraut-openai]

Addresses #22101

Why

Side conversations are ephemeral forks of the active thread, but /side was building its fork config from the app-level config after refreshing it from disk. If the parent thread had runtime settings that differed from the current persisted defaults, such as a changed model, reasoning effort, permissions, reviewer, or fast-mode selection, the side conversation could start with different behavior than its parent.

What changed

• Build side fork config from the active parent ChatWidget config, then overlay the parent thread's effective model, reasoning effort, service tier, and fast-mode opt-out state.
• Forward model reasoning summary, verbosity, personality, web search mode, and service-tier overrides through TUI app-server start/resume/fork lifecycle params.
• Add focused tests for parent runtime inheritance, side developer guardrail preservation, and lifecycle param forwarding.

[fcoury-oai]

Shared a finding from Codex for your consideration, other than that looks good.

I tested it by changing the model and reasoning on ~/.codex/config.toml after a session had started but before sending /side and it inherited the session settings, not what was in the config.