feat(management): add AI provider admin CRUD

[flooryyyy]

Motivation

• Provide workspace admins an integrated place to manage AI/model providers (enable/disable, set default, test connection) using the same provider-settings UX patterns as other management pages.
• Persist provider configuration in system settings so workspace AI features can use a configurable provider list.

Description

• Add a new management tab and UI section AiProvidersSection at src/app/(main)/management/AiProvidersSection.tsx and wire it into ManagementClient.tsx and the Sidebar under the #ai-providers anchor.
• Implement REST admin endpoints under src/app/api/management/ai-providers for list/create/update/delete, set default ([id]/default), and connection testing ([id]/test), reusing adminAction auth helper.
• Persist provider configs in systemSettings.aiProvidersJson with helpers in _lib.ts, add a DB migration src/app/db/migrations/34AddAiProvidersJson.ts, and update DB typings in src/app/lib/types/db.ts.
• Test connection logic includes lightweight checks for OpenAI, Anthropic and Google (Generative Language) endpoints and normalizes provider data (default enforcement, ids, required fields).

Testing

• Ran static/type checks: npm run -s check completed successfully (TypeScript types updated and verified).
• Ran unit tests: vitest run executed (run by the pre-commit hook) and all tests passed.
• Verified the management UI builds and the new API routes conform to the existing adminAction authorization wrapper during local checks.

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Codex Task