Chore/cleanup studio deps (#47399)

## Problem

Knip reported some unused dependencies. Some are actually used in
builds, etc but others are not.

## Solution

Remove the really unused dependencies

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

## Summary by CodeRabbit

* **Chores**
* Cleaned up unused dependencies and removed some obsolete test/support
files.
* Updated project ignore rules to better match current app structure and
generated files.
* **Bug Fixes**
* No user-facing behavior changed; this release is focused on
maintenance and cleanup.

<!-- end of auto-generated comment: release notes by coderabbit.ai -->

apps/studio/package.json

@@ -62,9 +62,6 @@
     "@monaco-editor/react": "catalog:",
     "@next/bundle-analyzer": "16.2.3",
     "@number-flow/react": "^0.3.2",
-    "@radix-ui/react-slider": "^1.1.2",
-    "@radix-ui/react-slot": "^1.2.0",
-    "@radix-ui/react-visually-hidden": "^1.2.3",
     "@sentry/nextjs": "catalog:",
     "@sentry/react": "^10.27.0",
     "@std/path": "npm:@jsr/std__path@^1.0.8",
@@ -75,7 +72,6 @@
     "@supabase/pg-meta": "workspace:*",
     "@supabase/realtime-js": "catalog:",
     "@supabase/shared-types": "0.1.88",
-    "@supabase/sql-to-rest": "^0.1.6",
     "@supabase/supabase-js": "catalog:",
     "@tanstack/react-devtools": "^0.10.3",
     "@tanstack/react-hotkeys": "^0.10.0",
@@ -113,13 +109,11 @@
     "http-status": "^2.1.0",
     "icons": "workspace:*",
     "idb": "^8.0.2",
-    "immutability-helper": "^3.1.1",
     "ip-num": "^1.5.1",
     "json-logic-js": "^2.0.2",
     "lodash": "catalog:",
     "lucide-react": "^0.436.0",
     "markdown-table": "^3.0.3",
-    "memoize-one": "^5.0.1",
     "mime-db": "^1.53.0",
     "monaco-editor": "catalog:",
     "next": "catalog:",
@@ -129,7 +123,6 @@
     "openapi-fetch": "0.12.4",
     "papaparse": "^5.3.1",
     "path-to-regexp": "^8.0.0",
-    "pg-minify": "^1.6.3",
     "radix-ui": "catalog:",
     "randombytes": "^2.1.0",
     "react": "catalog:",
@@ -150,7 +143,6 @@
     "shared-data": "workspace:*",
     "sonner": "^1.5.0",
     "sql-formatter": "^15.0.0",
-    "sqlstring": "^2.3.2",
     "streamdown": "^1.3.0",
     "@stripe/sync-engine": "1.0.32",
     "swiper": "^12.1.2",
@@ -171,7 +163,6 @@
     "@graphql-typed-document-node/core": "^3.2.0",
     "@radix-ui/react-use-escape-keydown": "^1.1.1",
     "@smithy/property-provider": "^4.0.4",
-    "@tailwindcss/container-queries": "^0.1.1",
     "@tailwindcss/vite": "4.2.4",
     "@tanstack/devtools-vite": "^0.6.0",
     "@testing-library/dom": "^10.0.0",
@@ -183,19 +174,14 @@
     "@types/file-saver": "^2.0.2",
     "@types/json-logic-js": "^1.2.1",
     "@types/lodash": "^4.14.172",
-    "@types/markdown-table": "^3.0.0",
     "@types/mime-db": "^1.43.5",
     "@types/node": "catalog:",
     "@types/papaparse": "^5.3.1",
     "@types/randombytes": "^2.0.3",
     "@types/react": "catalog:",
-    "@types/react-beautiful-dnd": "^13.1.2",
-    "@types/react-datepicker": "^4.3.4",
     "@types/react-dom": "catalog:",
     "@types/react-grid-layout": "^1.3.0",
     "@types/react-simple-maps": "^3.0.1",
-    "@types/recharts": "^1.8.23",
-    "@types/sqlstring": "^2.3.0",
     "@types/zxcvbn": "^4.4.1",
     "@vercel/config": "^0.2.1",
     "@vitejs/plugin-react": "catalog:",
@@ -220,7 +206,6 @@
     "postcss": "catalog:",
     "raw-loader": "^4.0.2",
     "require-in-the-middle": "^8.0.0",
-    "tailwindcss": "catalog:",
     "tsconfig": "workspace:*",
     "tsx": "catalog:",
     "typescript": "catalog:",