fix: drop transitive Zod 3 via type-only @ag-ui/core@0.1.0

[tombeckenham]

Important

Blocked on the @ag-ui/core@0.1.0 npm release. The upstream extraction of zod from @ag-ui/core is ag-ui-protocol/ag-ui#1637; we resolved its merge conflicts in ag-ui-protocol/ag-ui#1918. Once 0.1.0 is published: regenerate pnpm-lock.yaml, mark ready for review.

🎯 Changes

Fixes #520.

@ag-ui/core@0.0.x infers its public types from Zod 3 schemas and carries zod ^3.22 as a hard runtime dependency, dragging Zod 3 into every consumer's tree and type graph. Apps on Zod 4 (e.g. with @hookform/resolvers@5) hit zod/v4/core version-mismatch errors (TS2769: The types of '_zod.version.minor' are incompatible) when their lockfile resolves the resolver's zod/v4 import to Zod 3.25's shim.

@ag-ui/core@0.1.0 makes the main entry type-only with zero runtime dependencies and moves the zod schemas to an opt-in /schemas subpath (zod ^3.24 || ^4 optional peer). This PR:

• Bumps @ag-ui/core to ^0.1.0 — Zod 3 disappears from consumer installs entirely
• Loads RunAgentInputSchema lazily from @ag-ui/core/schemas inside chatParamsFromRequestBody, typed against a local structural interface so zod never appears in this package's compilation or its public .d.ts (the subpath's emitted declarations are pinned to one zod major; ours must not be)
• Declares zod (^3.24.0 || ^4.0.0) as an optional peer of @tanstack/ai: only server code calling chatParamsFromRequest* needs it; calling without zod rejects with an actionable AGUIError. Wire behavior unchanged.
• Updates the migration doc, chatParamsFromRequest API doc, and the ag-ui-protocol agent skill

Verification (against packed builds)

Scenario	Result
@tanstack/ai@latest (control): zod 4 + @hookform/resolvers@5 consumer	npm ls zod shows nested zod@3.25.76 under @ag-ui/core
Patched: same consumer	exactly one zod@4.4.3 in the whole tree; tsc --noEmit clean with skipLibCheck: false
Patched: runtime	chatParamsFromRequestBody parses valid bodies (incl. parts re-attach) and rejects invalid ones with AGUIError, validated by upstream schemas running on zod 4
Patched: consumer with no zod	import '@tanstack/ai' works; calling chatParamsFromRequest* rejects with the install-zod message

✅ Checklist

• I have followed the steps in the Contributing guide.
• I have tested this code locally with pnpm run test:pr. (Run with @ag-ui/core pointed at a tarball built from ag-ui#1918, since 0.1.0 isn't published yet — all targets green, incl. unit (1003), types, lint, knip, sherif, docs, publint, build. E2E: 259 passed, 4 flaky multimodal-image retries unrelated to this change.)

🚀 Release Impact

• This change affects published code, and I have generated a changeset.
• This change is docs/CI/dev-only (no release).

🤖 Generated with Claude Code

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