fix: align web packages with master's two-stage build layout

The web packages were authored against the old single-stage layout where
tsc emitted directly to lib/. Master compiles declarations to lib/types/
via tsc -b, then bundles JS into lib/ via tsdown. Point every web package's
tsc outDir at lib/types, update package.json types/exports/files to the
lib/types declaration + lib/ bundle shape (matching dsh-bash/dsh-tool-bash),
and bundle tool-web's subpath entries from lib/types/*.js rather than src.

packages/web/web-search-perplexity/tsconfig.json

@@ -2,7 +2,7 @@
   "extends": "../../../tsconfig.base.json",
   "compilerOptions": {
     "rootDir": "src",
-    "outDir": "lib"
+    "outDir": "lib/types"
   },
   "include": [
     "src"