refactor(tsconfig): single root solution graph over host/client aggregates

Root tsconfig.json becomes a pure solution (files:[] + two references);
the former root host aggregate moves verbatim to tsconfig.host.json.
New tsconfig.base.client.json carries the shared client compiler shape
(jsx/DOM lib/types:[]), and tsconfig.client.json plus the 12
packages/client tsconfigs extend it instead of restating the trio.
tsconfig.build.json is deleted: the solution covers the full emit graph,
absorbing the command-goal typecheck/build drift.

Consumers migrate to the single graph: typecheck/build scripts and the
lefthook pre-push hook run bare `tsc -b` (pre-push now covers the client
side); the run-gates build gate needs typecheck so two concurrent tsc -b
runs cannot race the same tsbuildinfo; ts-project.ts and the standalone
doc-typecheck mode seed tsconfig.host.json explicitly (never the root
solution — flattening host+client into one program collides the cordis
Context merges); verify-cordis-config BFS seeds the root solution alone.

Per missions/tsconfig-single-graph-migration.md §2–§3.

tsconfig.client.json

@@ -4,14 +4,13 @@
   // under the same keys (sessions, loader) with different services; shared
   // leaves (session/llm/tools/apiproxy/...) build once and are referenced by
   // both programs through each client package's own references.
-  "extends": "./tsconfig.base.json",
+  "extends": "./tsconfig.base.client.json",
   "compilerOptions": {
     "noEmit": true,
     "rewriteRelativeImportExtensions": false,
-    "jsx": "react-jsx",
-    "lib": ["ES2024", "DOM", "DOM.Iterable"],
     // Tests execute under vitest on node (e2e files spawn processes); browser
-    // purity of package src is each package's own tsconfig + verify-client-closure.
+    // purity of package src is each package's own tsconfig plus
+    // scripts/client-bundle-purity.spec.ts.
     "types": ["node"]
   },
   "include": [