Speed up full integration with parallel agent lanes

[rohita5l]

Summary

Replace the six serial full-integration shards with two parallel agent lanes: one Claude VM and one Codex VM. Each lane installs its agent once and runs every case for that agent serially.

The last successful #606 CI run took 14m18s, including 10m50s from the first full-journey job starting to the last one finishing:
https://github.com/databricks/unity-gateway/actions/runs/34920527726

The first revision passed all checks in 8m19s: 5m59s / 42% less time than that baseline, retaining all 39 live cases:
https://github.com/databricks/unity-gateway/actions/runs/34921778894

The follow-up also starts integration immediately alongside unit/agent e2e tests, removing the remaining agent-e2e startup barrier. The final required merge gate still waits for both suites and requires both to succeed. The new revision's CI will validate the additional speedup and increased request overlap.

Coverage and safety

• Preserve all 39 live cases: Claude 15, Codex 24. A local collection audit verified that each lane exactly equals the union of its previous three shards, and that the lanes are disjoint and cover every live case.
• Keep all four smoke cases, all three installation checks, and manual TUI selection of all four TUI cases.
• Unit tests, agent e2e, and integration start independently. Keep integration's smoke → full barrier, fail-fast: false, per-case isolation/cleanup, evidence uploads, and the required test / e2e merge gates.
• At most one full-suite job per agent within a run. Agent e2e and other PRs still share workspace capacity; this is not a global quota guarantee.
• No test removals, new skips, retries, weakened assertions, sandbox changes, production-code changes, or dependency changes.
• Update job/artifact names and local reproduction documentation for the two lanes.

Validation

• Clean local Linux ordinary suite: 2,185 passed, 47 existing skips. No live integration pass is claimed by that run.
• Exact pytest collection comparison: 39/39 live cases retained, plus unchanged four-case smoke/TUI selections.
• Ruff check and format check passed.
• Actionlint with ShellCheck passed.
• git diff --check passed.
• Local workflow audit: immediate startup confirmed; all 16 success/failure/skipped/cancelled combinations checked against the final gate's actual shell command. Only two successful suites pass.
• First revision live CI: all checks and all 39 full-suite cases passed in 8m19s.
• Immediate-start revision live CI and timing: pending.