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/tanstack-react-query.md

@@ -0,0 +1,69 @@
+---
+package: "@trpc/tanstack-react-query"
+version: "^11.1.0"
+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/tanstack-react-query license
+accepted-cves: []
+---
+
+## Filter: license
+
+MIT — on the workspace allowlist.
+
+## Filter: types
+
+Ships first-party TypeScript types; part of the tRPC v11 adapter suite.
+
+## Filter: maintenance
+
+Active. Maintained by the tRPC team as part of the v11 TanStack Start integration.
+
+## Filter: boundary-fit
+
+Core package. Required for the TanStack Start provider (`core-trpc/tanstack`). No boundary rule violation.
+
+## Filter: shadow-check
+
+No duplicate TanStack adapter 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` exposes a TanStack Start provider via `@trpc/tanstack-react-query` for `apps/web-tanstack`.
+
+## Prompt: replaces
+
+Nothing — this is the initial tRPC scaffold.
+
+## Prompt: migration-cost-out
+
+Hard: the TanStack provider is shaped around this adapter's API; replacing requires re-implementing the provider.
+
+## Prompt: alternatives-considered
+
+This is the official tRPC adapter for TanStack Start. No viable alternative exists.