fix: respect TUI variant (ctrl+t) and inherit it for auto prompts

[Hisir0909]

Summary

• Ensures user-selected variant (ctrl+t / variant_cycle) is never overridden by plugin defaults, including on the first message of a new session
• Makes auto-generated prompts (background task completion + atlas continuation) inherit the parent session’s variant for consistent reasoning level

Changes

• keyword-detector: respect input.variant and use provider/model-aware ultrawork variant inference only as fallback
• background-agent: include parent variant when sending completion notifications to the parent session
• atlas: include parent variant when injecting boulder continuation prompts
• index: centralize chat.message variant precedence logic to prevent first-message gate from overriding ctrl+t selection
• tests: add coverage for variant precedence and inheritance scenarios

Testing

bun run typecheck
bun test

Related Issues

Closes #521

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Summary by cubic

Respect the user-selected reasoning variant (Ctrl+T) across all messages and make auto-generated prompts inherit the parent session’s variant. Centralizes variant precedence to prevent defaults from overriding user choice and improves ultrawork variant inference.

• Bug Fixes

  • Preserve input.variant on all chat messages, including the first in a new session.
  • Auto prompts (background task completion, atlas continuation) inherit the parent session’s variant.
  • Keyword detector respects input.variant and infers ultrawork variant by model/provider when unset.

• Refactors

  • Centralized variant precedence in shared/chat-message-variant and applied it in index.
  • Added tests for variant precedence and inheritance across keyword-detector, atlas, and background-agent.

^{Written for commit e93525c. Summary will update on new commits.}

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[Hisir0909]

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[cubic-dev-ai]

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