Remove root eslintrc from basic example. (#8423)

### Description

Some small examples fixes:
- `basic` to line up with best practices
- `with-berry` because the lockfile somehow got broken?

examples/basic/package.json

@@ -8,8 +8,6 @@
     "format": "prettier --write \"**/*.{ts,tsx,md}\""
   },
   "devDependencies": {
-    "@repo/eslint-config": "workspace:*",
-    "@repo/typescript-config": "workspace:*",
     "prettier": "^3.2.5",
     "turbo": "^2.0.3",
     "typescript": "^5.4.5"

examples/with-berry/yarn.lock

@@ -4424,17 +4424,6 @@ __metadata:
   languageName: node
   linkType: hard
 
-"root-workspace-0b6124@workspace:.":
-  version: 0.0.0-use.local
-  resolution: "root-workspace-0b6124@workspace:."
-  dependencies:
-    eslint: 8.57.0
-    eslint-config-custom: "*"
-    prettier: ^3.2.5
-    turbo: ^2.0.3
-  languageName: unknown
-  linkType: soft
-
 "run-applescript@npm:^5.0.0":
   version: 5.0.0
   resolution: "run-applescript@npm:5.0.0"
@@ -5295,6 +5284,17 @@ __metadata:
   languageName: node
   linkType: hard
 
+"with-berry@workspace:.":
+  version: 0.0.0-use.local
+  resolution: "with-berry@workspace:."
+  dependencies:
+    eslint: 8.57.0
+    eslint-config-custom: "*"
+    prettier: ^3.2.5
+    turbo: ^2.0.3
+  languageName: unknown
+  linkType: soft
+
 "wrap-ansi-cjs@npm:wrap-ansi@^7.0.0":
   version: 7.0.0
   resolution: "wrap-ansi@npm:7.0.0"