fix(pi): use native Responses models safely

[dgokeeffe]

Summary

• route Pi GPT and Grok models through AI Gateway's native Responses API
• classify shared GPT/Grok capabilities and render supported reasoning metadata
• use Pi's standard configuration directory with collision-safe backup migration
• retain supplemental Claude versions and thinking metadata needed by Pi

Why

Pi's generated model catalogue had drifted from the protocols and models actually exposed by AI Gateway. Valid models could be hidden or sent to an incompatible route, while upgrading from ucode's former private Pi directory could restore an unrelated legacy backup over the user's standard configuration.

This establishes the safe Pi foundation used by the later discovery and OSS-streaming PRs.

Stack

PR A of five. This PR is based directly on main and is the first reviewable change.

Planned dependency order: A → B → C → D and E.

• A: #446 — this PR
• B: #447 — Claude discovery hardening
• C: #448 — capability-driven discovery
• D: #449 — Pi OSS streaming
• E: #450 — OpenCode native Responses routing

Validation

• 372 focused Pi/config/CLI tests passed
• Ruff lint and changed-file formatting passed
• ty check src passed
• git diff --check passed
• the complete integration stack passed 2,358 tests with 37 skips; its three failures reproduce unchanged on main
• fresh installed-build Pi inference passed against a validated OSS model, including proxy URL and listener cleanup

Non-goals

This PR does not add the MLflow OSS streaming provider or change OpenCode routing; those are isolated later in the stack.