Remove "push" script and task (#4762)

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## PR-Codex overview
This PR focuses on modifying the `turbo.json` and `package.json` configuration files, specifically removing certain caching options and adjusting command scripts related to the build process.

### Detailed summary
- In `turbo.json`, removed the `push` configuration and its `cache` and `dependsOn` settings.
- In `package.json`, removed the `push` script that executed `turbo run push --filter=./packages/*`.

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package.json

@@ -36,7 +36,6 @@
     "release": "node ./scripts/pre-release.mjs && turbo run update-version && pnpm build:release && changeset publish",
     "version-packages:nightly": "node scripts/pre-nightly.mjs && changeset version --snapshot nightly",
     "release:nightly": "node ./scripts/pre-release.mjs && turbo run update-version && pnpm build && changeset publish --tag nightly",
-    "push": "turbo run push --filter=./packages/*",
     "hotlink-init": "node ./scripts/hotlink/hotlink-init.mjs",
     "hotlink-revert": "node ./scripts/hotlink/hotlink-revert.mjs"
   },

turbo.json

@@ -84,10 +84,6 @@
     },
     "clean": {
       "cache": false
-    },
-    "push": {
-      "cache": false,
-      "dependsOn": ["build"]
     }
   }
 }