feat: add Requesty as an OpenAI-compatible provider

[Thibaultjaigu]

What

Adds Requesty as a named, OpenAI-compatible LLM provider, mirroring the existing OpenRouter provider end-to-end (both local browser-direct mode and the server-side proxy mode).

Requesty (https://requesty.ai) is an OpenAI-compatible LLM gateway. It uses the same provider/model naming as OpenRouter (e.g. openai/gpt-4o-mini) and is reachable at https://router.requesty.ai.

Changes

Mirrors each site where OpenRouter is wired, with no new dependencies (@openrouter/ai-sdk-provider is reused since Requesty is OpenAI-compatible) and no new translation strings (reuses existing generic setting keys):

• src/constants/urls.ts — REQUESTY_BASE_URL.
• src/utils/deep-research/provider.ts — requesty branch in the provider factory.
• src/app/api/ai/requesty/[...slug]/route.ts — server proxy route (new), mirroring the OpenRouter route.
• src/store/setting.ts — requestyApiKey / requestyApiProxy / requestyThinkingModel / requestyNetworkingModel fields + defaults.
• src/hooks/useAiProvider.ts — provider-creation, model resolution, and has-key sites.
• src/hooks/useModelList.ts — Requesty model-list fetch.
• src/components/Setting.tsx — provider picker entry, API key/proxy form, thinking/networking model pickers, and the zod schema fields.
• src/app/api/utils.ts, src/middleware.ts, next.config.ts — proxy-mode base URL/key resolution, auth + key injection, and rewrite rule.
• env.tpl — REQUESTY_API_KEY / REQUESTY_API_BASE_URL.

Testing

• tsc --noEmit — clean (0 errors) after pnpm install.
• Live check against the real endpoint: POST https://router.requesty.ai/v1/chat/completions with openai/gpt-4o-mini → HTTP 200 with a valid completion.

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I work at Requesty. This mirrors the existing OpenRouter provider as closely as possible. Happy to adjust wording/placement or close it if it's not a fit.