feat(core-trpc): scaffold tRPC client with React Query providers

- createTRPCContext + useTRPC hook for typed client access
- NextTrpcProvider with SSR-safe absolute URL resolution
- TanstackTrpcProvider for TanStack Start apps
- /api/trpc catch-all route handler in web-next
- Wire NextTrpcProvider into app providers
- Add @repo/core-trpc to transpilePackages

docs/library-decisions/2026-05-14-@trpc/react-query.md

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+---
+package: "@trpc/react-query"
+version: "^11.0.0"
+tier: core
+decision: approved
+date: 2026-05-14
+deciders: [scaffolded]
+adr: null
+is-sub-processor: false
+processes-pii: false
+filter-results:
+  license: MIT
+  types: native
+  maintenance: active
+  boundary-fit: pass
+  shadow-check: pass
+  eu-residency: n/a
+  cve-scan: clean
+  named-consumer: pass
+  socketRisk: skip
+verification-commands:
+  - pnpm audit --audit-level=moderate
+  - npm view @trpc/react-query license
+accepted-cves: []
+---
+
+## Filter: license
+
+MIT — on the workspace allowlist.
+
+## Filter: types
+
+Ships first-party TypeScript types; deeply integrated with tRPC's type inference.
+
+## Filter: maintenance
+
+Active. Maintained by the tRPC team alongside `@trpc/server` and `@trpc/client`.
+
+## Filter: boundary-fit
+
+Core package. The React Query integration bridge belongs in `core-trpc` alongside its sibling tRPC packages. No boundary rule violation.
+
+## Filter: shadow-check
+
+No other tRPC–React Query bridge in the workspace. No shadow.
+
+## Filter: eu-residency
+
+Client-side integration adapter; no vendor data transmission. n/a.
+
+## Filter: cve-scan
+
+No advisories at adoption time.
+
+## Filter: named-consumer
+
+`core-trpc` re-exports `@trpc/react-query` hooks for use in Next.js feature pages.
+
+## Prompt: replaces
+
+Nothing — this is the initial tRPC scaffold.
+
+## Prompt: migration-cost-out
+
+Hard: hooks are tRPC-procedure-typed; migrating away requires replacing all call sites.
+
+## Prompt: alternatives-considered
+
+This package is the canonical integration point between `@trpc/client` and `@tanstack/react-query`. No viable alternative exists.