feat(ai): replace OpenCode Zen with AI Gateway

[Aditya190803]

Generation now uses AI Gateway's OpenAI-compatible chat endpoint instead of OpenCode Zen across resume analysis, cover letters, resume generation, LaTeX repair, and interview preparation. Health checks use the same gateway configuration.

• Replace provider environment variables with AI_GATEWAY_API_KEY and optional AI_GATEWAY_BASE_URL; keep MODEL_NAME configurable and preserve provider/vendor prefixes.
• Preserve existing prompts, temperatures, normalization, caching, and interview retries. Add fetch cancellation for the configured timeout and exclude upstream error bodies from failures.
• Update deployment checks, .env.example, README, and agent instructions. Add transport and health-check regression coverage.

Depends on #10 (feat/ui-overhaul). Merge the parent before this PR.

Validation: vp install --frozen-lockfile, vp check, vp run lint, and vp run typecheck passed; targeted gateway/generation/health tests: 27 passed. Full suite: 56 files / 348 tests passed; coverage thresholds passed (65.28% statements, 59.29% branches, 62.81% functions, 66.05% lines). vp run build passed.

Setup: create a managed gateway key and choose a chat-capable model available to it via /v1/models. The default is the documented claude-sonnet-5 example. Replace legacy OpenCode environment settings in deployment. Connected Codex subscription seats require /v1/responses, so choose a chat-capable provider for this integration. An authenticated gateway call was not exercised because no managed key is configured locally.

Gateway documentation: https://ai-gateway.adityamer.dev/docs

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Project	Deployment	Actions	Updated
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