feat(clients): add PR auto-settle toggle

[caezium]

What Changed

• Add an independent setting for settling Sidebar v2 threads when their pull request is merged or closed, enabled by default for backward compatibility.
• Gate the shared settlement calculation on that setting while preserving manual settlement, explicit un-settlement, pending-work guards, and inactivity-based settlement.
• Expose the control on web/desktop and mobile, and document how disabling both automatic triggers enables fully manual settlement.

Closes #4982.

Why

Sidebar v2 previously classified merged and closed pull-request threads as settled unconditionally. Disabling “Auto-settle inactive threads” therefore could not keep those threads active for follow-up work.

The merged/closed trigger is now configurable independently from the inactivity trigger. Existing users keep the current behavior unless they opt out.

UI Changes

Before

The inactivity setting also stated that merged and closed PR threads always settle, with no separate control.

After

A separate toggle controls merged/closed-PR settlement. Here it is disabled while inactivity-based settlement remains enabled.

Validation

• bun test packages/contracts/src/settings.test.ts packages/client-runtime/src/state/threadSettled.test.ts apps/mobile/src/features/threads/threadListV2.test.ts — 250 passed
• bun --cwd apps/desktop test -- DesktopClientSettings.test.ts — 7 passed
• Typechecks passed for contracts, client runtime, web, and mobile
• Targeted lint and formatting checks passed for all 16 changed files
• Verified in an empty, isolated local T3 home that the setting defaults on, persists off across reload, remains independent from inactivity settlement, and persists when re-enabled

Checklist

• This PR is small and focused
• I explained what changed and why
• I included before/after screenshots for the UI change
• No animation or timing behavior changed, so a video is not applicable

Built with GPT-5.6-Sol via the Codex harness in T3 Code.

Note

Add PR auto-settle toggle to client settings, web sidebar, and mobile thread list

• Adds sidebarAutoSettleOnChangeRequestCompletion to ClientSettingsSchema (default true) and exposes a toggle in the web beta settings panel, allowing users to disable automatic settlement when a PR is merged or closed.
• Extends effectiveSettled in threadSettled.ts to accept autoSettleOnChangeRequestCompletion; when false, merged/closed PRs no longer trigger settlement.
• Adds two new mobile preferences (threadListV2AutoSettleInactive, threadListV2AutoSettleOnChangeRequestCompletion) read by a new useThreadListV2SettlementPreferences hook and surfaced as independent toggles in the mobile beta settings UI.
• Behavioral Change: existing users retain current auto-settle behavior (both flags default to true), but the new settings are device-local on mobile and client-scoped on web.

^{Macroscope summarized 1f2d7cb.}

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[macroscopeapp]

Approvability

Verdict: Needs human review

This PR introduces a new user-facing feature adding toggles to control auto-settlement of PR threads. Changes to core workflow behavior (the effectiveSettled logic) and new settings UI across web and mobile platforms warrant human review.

^{You can customize Macroscope's approvability policy. Learn more.}