chore: finish moving the toolchain off bun

The check job still installed bun to typecheck, the generated docs page
still told self-hosters to run bun install/bunx, and bun.lock sat next
to package-lock.json with nothing reading it. Switch CI to setup-node
plus npm workspaces, update the self-hosting snippet in the docs
generator, delete the stale lockfile, and bump webapp to the vitest
test runner.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01GaLeuxVikb3iH2Etw2tHe7

Author: codebam

.github/workflows/deploy.yml

@@ -23,14 +23,14 @@ jobs:
       - uses: actions/checkout@v4
         with:
           submodules: recursive
-      - uses: oven-sh/setup-bun@v2
+      - uses: actions/setup-node@v4
         with:
-          bun-version: latest
-      - run: bun install --frozen-lockfile
+          node-version: 22
+      - run: npm install
       - name: Typecheck shared
-        run: bun run --cwd packages/shared check
+        run: npm run check --workspace packages/shared
       - name: Typecheck bot
-        run: bun run --cwd bot check
+        run: npm run check --workspace bot
 
   deploy_bot_dev:
     if: github.event_name == 'push' && !startsWith(github.ref, 'refs/tags/')