[codex] update OpenAI Codex models

[romgenie]

Summary

• Update the bundled Codex model list for the newly published GPT-5.6 family.
• Make gpt-5.6-sol the Codex default and gpt-5.6-luna the small/fast fallback.
• Refresh docs, picker labels, onboarding copy, slash-command help, and managed-agent presets.
• Fix the locked clippy lint triggered by the current toolchain on Anthropic bearer header formatting.
• Stabilize the TUI provider picker test without mutating the core test-home override.

Context

• Related issue/user request: update OpenAI/Codex models after new models were added today.
• Scope: Codex/OpenAI model IDs, metadata, default selection, UI/help/docs references, and CI fixes blocking this PR.
• Non-goals: adding a standalone OpenAI API provider or changing Anthropic model selection.

Changes

• Add gpt-5.6-sol, gpt-5.6-terra, and gpt-5.6-luna to the curated Codex OAuth model list.
• Update Codex provider metadata to give the GPT-5.6 models 1.05M context and 128K max output.
• Prioritize GPT-5.6 models in registry heuristics and assert the Codex default/small fallbacks in tests.
• Update provider docs and user-facing strings from gpt-5.5 to gpt-5.6-sol where they describe the default.
• Remove redundant borrows in two bearer-auth format! calls so locked clippy passes.
• Use COVEN_CODE_CLAUDE_BIN in the provider picker test for deterministic local Claude CLI discovery.
• Stop mutating COVEN_CODE_TEST_HOME from the TUI test guard so workspace test binaries do not race with core hosted-memory tests.

Validation

Record exact commands and outcomes. Mark items N/A with a reason when they do not apply.

• git diff --check - passed.
• cargo fmt --all - passed.
• cargo check --workspace - passed.
• cargo clippy --workspace --all-targets -- -D warnings - passed before the CI lint report.
• cargo clippy --workspace --all-targets --locked -- -D warnings - passed after the CI lint report and after the test-home race fix.
• cargo test --workspace --locked --quiet - passed after the test-home race fix.
• Targeted/manual checks:
  • cargo test --package claurst-core codex - passed.
  • cargo test --package claurst-api codex_best_models_return_real_ids_without_snapshot - passed.
  • cargo test --package claurst-tui models_for_provider_codex - passed.
  • cargo test --package claurst-tui --lib - passed.
  • cargo test --package claurst-tui provider_picker_marks_claude_cli_local_when_binary_exists -- --nocapture - passed.
• Not run: no remaining skipped checks for the touched Rust paths.

PR Readiness

• Diff is limited to the intended files.
• Generated files were not edited by hand.
• User-facing docs/help were updated or are not needed.
• No secrets, credentials, local paths, or unrelated logs are included.
• Remaining risks or follow-up work are listed above.

Remaining risk: Codex availability is based on official OpenAI documentation; runtime access can still depend on ChatGPT account entitlement. Vercel may still require deployment authorization outside this code change.

[vercel]

@romgenie is attempting to deploy a commit to the 0xBuns Team on Vercel.

A member of the Team first needs to authorize it.

[romgenie]

@BunsDev please review. This updates the Codex model catalog to GPT-5.6 Sol/Terra/Luna, makes Sol the default, and sets Luna as the fast/small fallback.