[Feat] Add Z.AI and Z.AI Coding Plan inference providers

[pridemusvaire]

Summary

Adds Z.AI and Z.AI Coding Plan as first-class BYOK inference providers, with an International / China region select on connect instead of four separate catalog rows.

• Catalog ids: zai, zai-coding-plan
• Model ids: zai/glm-5.2, zai-coding-plan/glm-5.2 (region-independent)
• Env: ZAI_API_KEY + ZAI_REGION, ZAI_CODING_PLAN_API_KEY + ZAI_CODING_PLAN_REGION (global | china, default global)
• Inference gateway uses models.dev v4 bases and /chat/completions paths (not OpenAI /v1/...)
• Connect UI supports selectable additionalEnvFields.options (region select)

Test plan

• pnpm --filter @roomote/types exec vitest run src/model-provider-config.test.ts src/__tests__/inference-gateway.test.ts (83 passed)
• pnpm --filter @roomote/api exec vitest run src/handlers/inference/__tests__/inference-gateway.test.ts (43 passed)
• Pre-push: check-types:fast, lint, knip

[roomote-roomote]

No code issues found. See task

• apps/docs/environment-variables.mdx:186 Document ZAI_API_KEY, ZAI_REGION, ZAI_CODING_PLAN_API_KEY, and ZAI_CODING_PLAN_REGION alongside the other inference provider settings. The new providers are available to self-hosted deployments, but their required configuration is absent from the public environment-variable reference; the provider listings and env-forwarding guidance in apps/docs/models.mdx, SELF_HOSTING.md, and README.md should be kept in sync as well.

_{Reviewed cc763d}

[github-actions]

All contributors have signed the CLA.
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[pridemusvaire]

I have read the CLA Document and I hereby sign the CLA

[mrubens]

Thanks for the PR! I just pushed a small cleanup and will merge once the tests and review come back clean.

[pridemusvaire]

thanks @mrubens , I love the product, great work.