chore: migrate repo to pnpm v11 (#48033)

## I have read the
[CONTRIBUTING.md](https://github.com/supabase/supabase/blob/master/CONTRIBUTING.md)
file.

YES

## What kind of change does this PR introduce?

Chore / dependency tooling update.

## What is the current behavior?

The repo is pinned to pnpm 10.24.0. Closes
https://linear.app/supabase/issue/FE-3673/migrate-the-repo-to-use-pnpm-v11.

## What is the new behavior?

The repo is pinned to pnpm 11.13.1, pnpm v11 workspace settings are
migrated to `allowBuilds`, and the Studio Dockerfile installs pnpm
11.13.1.

## Additional context

Validated with `CI=true mise exec node@22 -- pnpm install
--frozen-lockfile`, `mise exec node@22 -- pnpm run typecheck`, and `mise
exec node@22 -- pnpm run lint`; full Prettier check still fails on
existing generated docs/router files outside this migration.


<!-- This is an auto-generated comment: release notes by coderabbit.ai
-->
## Summary by CodeRabbit

* **Chores**
* Updated tooling requirements (pnpm **11.13.1**, Node **>=22.13**) and
aligned container build tooling accordingly.
* Adjusted package manager behavior (scoped registry override, update
notifications disabled) and workspace build/engine validation settings.

* **Maintenance**
* Updated `clean` scripts across apps/packages to remove only
build/cache artifacts (no longer delete installed dependencies).
* Reduced Turbo `clean` task output to **errors-only** for cleaner logs.
<!-- end of auto-generated comment: release notes by coderabbit.ai -->

package.json

@@ -12,7 +12,7 @@
     "build:studio:docker": "docker build . -f apps/studio/Dockerfile --target production -t supabase-studio:local --build-arg NEXT_PUBLIC_STUDIO_AUTH_MODE=supabase --no-cache",
     "build:design-system": "turbo run build --filter=design-system",
     "build:docs": "turbo run build --filter=docs",
-    "clean": "turbo run clean --parallel && rimraf -G node_modules/{*,.bin,.modules.yaml} .turbo/cache",
+    "clean": "turbo run clean --parallel && rimraf -G .turbo/cache && pnpm purge",
     "dev": "turbo run dev --parallel",
     "dev:studio": "turbo run dev --filter=studio --parallel",
     "dev:studio-local": "pnpm setup:cli && NODE_ENV=test MODE=test pnpm --prefix ./apps/studio dev",
@@ -65,8 +65,8 @@
     "url": "git+https://github.com/supabase/supabase.git"
   },
   "engines": {
-    "pnpm": "10.24",
-    "node": ">=22"
+    "pnpm": "11.13",
+    "node": ">=22.13"
   },
   "keywords": [
     "postgres",
@@ -76,5 +76,5 @@
     "database",
     "auth"
   ],
-  "packageManager": "pnpm@10.24.0"
+  "packageManager": "pnpm@11.13.1"
 }