Use shared release action (#3994)

## Description

Removes release scripts and related tests and uses [shared publish
action](https://github.com/software-mansion-labs/npm-package-publish),
which uses the same scripts.

## Test plan

Tested it on a fork:
-
https://github.com/j-piasecki/react-native-gesture-handler/actions/runs/22343887406/job/64653421948
-
https://github.com/j-piasecki/react-native-gesture-handler/actions/runs/22344178991/job/64654420340

Author: j-piasecki

.github/actions/publish-npm-package/action.yml

@@ -42,17 +42,35 @@ jobs:
       - name: Check out
         uses: actions/checkout@v4
 
+      - name: Set up environment
+        shell: bash
+        run: |
+          echo "YARN_ENABLE_HARDENED_MODE=0" >> $GITHUB_ENV
+  
+      - name: Setup Node
+        uses: actions/setup-node@v6
+        with:
+          node-version: 24
+          cache: 'yarn'
+          registry-url: https://registry.npmjs.org/
+
       - name: Publish manual release
         if: ${{ github.event_name == 'workflow_dispatch' }}
-        uses: ./.github/actions/publish-npm-package
+        uses: software-mansion-labs/npm-package-publish@main
         with:
+          package-name: 'react-native-gesture-handler'
+          package-json-path: 'packages/react-native-gesture-handler/package.json'
+          install-dependencies-command: 'yarn install --immutable'
           release-type: ${{ inputs.release-type }}
           version: ${{ inputs.version }}
           dry-run: ${{ inputs.dry-run }}
 
       - name: Publish automatic nightly release
         if: ${{ github.event_name == 'schedule' }}
-        uses: ./.github/actions/publish-npm-package
+        uses: software-mansion-labs/npm-package-publish@main
         with:
+          package-name: 'react-native-gesture-handler'
+          package-json-path: 'packages/react-native-gesture-handler/package.json'
+          install-dependencies-command: 'yarn install --immutable'
           release-type: 'nightly'
           dry-run: false

.github/workflows/publish-release.yml

@@ -34,10 +34,5 @@ jobs:
       - name: Install node dependencies
         run: yarn --immutable
 
-      - name: Run jest scripts tests
-        run: yarn test:scripts
-
       - name: Run jest package tests
-        # always run this step even if the previous step fails
-        if: ${{ always() }}
         run: yarn workspace react-native-gesture-handler test

.github/workflows/run-jest-tests.yml

@@ -15,8 +15,7 @@
     "ts-check": "yarn workspaces foreach --all --parallel --topological-dev run ts-check",
     "lint-js": "yarn workspaces foreach --all --parallel --topological-dev run lint-js",
     "format-js": "yarn workspaces foreach --all --parallel --topological-dev run format-js",
-    "clean": "yarn workspaces foreach --all --parallel --topological-dev run clean && rm -rf node_modules yarn.lock",
-    "test:scripts": "jest ./scripts"
+    "clean": "yarn workspaces foreach --all --parallel --topological-dev run clean && rm -rf node_modules yarn.lock"
   },
   "devDependencies": {
     "@types/react": "^19.0.12",