chore(web): apply prettier 3.8 + Next 16 tsconfig auto-formatting

Side effects from `bun run format` (prettier 3.8) and `bun run build`
(Next 16) that I missed in the prior commit:

- web/components/ui/badge.tsx, web/components/ui/button.tsx: prettier 3.8
  inlines short interface `extends` lists onto a single line.
- web/tsconfig.json: Next 16's build step auto-modernizes tsconfig:
  `jsx: "preserve"` → `jsx: "react-jsx"` and reformats `lib`/`paths`
  arrays to multi-line. Build is identical either way; committing the
  modernized shape so subsequent `next build` runs do not produce
  spurious diffs.

web/tsconfig.json

@@ -11,7 +11,7 @@
     "moduleResolution": "bundler",
     "resolveJsonModule": true,
     "isolatedModules": true,
-    "jsx": "preserve",
+    "jsx": "react-jsx",
     "incremental": true,
     "noUncheckedIndexedAccess": true,
     "noUnusedLocals": true,