fix: use @ai-sdk/anthropic provider so ANTHROPIC_API_KEY works as documented

[erhnysr]

What this fixes

Following the README's own local setup instructions currently breaks every AI feature.

The README, .env.example, and the Vercel deploy button all tell you to provide ANTHROPIC_API_KEY. But both API routes reference the model as a bare string:

model: "anthropic/claude-sonnet-4-20250514"

In AI SDK v6, a bare-string model is resolved through the Vercel AI Gateway, which authenticates via AI_GATEWAY_API_KEY (or Vercel OIDC) and never reads ANTHROPIC_API_KEY. There is no @ai-sdk/anthropic dependency in the project, so the documented key has nothing to bind to.

Result: a developer who does exactly what the README says (cp .env.example .env.local, set ANTHROPIC_API_KEY, bun dev) gets an auth failure on every request:

Unauthenticated request to AI Gateway.
To authenticate, set the AI_GATEWAY_API_KEY environment variable with your API key.
Alternatively, you can use a provider module instead of the AI Gateway.

The fix

Add @ai-sdk/anthropic and use the provider module, which reads ANTHROPIC_API_KEY from the environment by default — matching the documented setup:

import { anthropic } from "@ai-sdk/anthropic"
// ...
model: anthropic("claude-sonnet-4-20250514")

Applied to both routes: app/api/agent/route.ts and app/api/agent/generate/route.ts.

The AI SDK's own gateway error even points at this exact remedy ("use a provider module instead of the AI Gateway").

Why this matches the intended setup

No docs change is needed — this makes the code honor the ANTHROPIC_API_KEY that the README and .env.example already document. The provider is pinned to @ai-sdk/anthropic@^3.0.102 (the package's ai-v6 release line) so it's spec-compatible with the pinned ai@6.0.37; the newer 4.x line targets a different AI SDK major and fails type-checking here.

Verification (local, per the README)

Set only ANTHROPIC_API_KEY in .env.local, bun dev, then POST /api/agent/generate:

	Model reference	Server-side result
Before	"anthropic/claude-sonnet-4-20250514"	Unauthenticated request to AI Gateway — ANTHROPIC_API_KEY ignored
After	anthropic("claude-sonnet-4-20250514")	request reaches Anthropic and uses the key as x-api-key (a real key returns a completion; a dummy key returns Anthropic's invalid x-api-key)

Also verified:

• bunx tsc --noEmit — clean
• bun run build — compiles successfully; both /api/agent and /api/agent/generate build as dynamic routes

Scope

Minimal: two one-line model changes + their import, one dependency, and the lockfile. No behavior change beyond authentication; system prompts, tools, validation, and rate limiting are untouched.

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