chore: Update yarn, refactor packages setup (#4085)

* Update yarn, refactor packages setup

* Rename some jobs in lib-check.yml

* Update website/yarn.lock

* Revert build-type-and-test job name change

.github/workflows/other-runtime-unit-test.yml

@@ -16,18 +16,10 @@ jobs:
       - uses: actions/setup-node@v4
         with:
           node-version: 18
+          cache: yarn
       - uses: denoland/setup-deno@v2
         with:
           deno-version: 'v2.1.x'
-      - name: Get yarn cache directory path
-        id: yarn-cache-dir-path
-        run: echo "dir=$(yarn config get cacheFolder)" >> $GITHUB_OUTPUT
-      - uses: actions/cache@v4
-        with:
-          path: ${{ steps.yarn-cache-dir-path.outputs.dir }}
-          key: ${{ runner.os }}-yarn-${{ hashFiles('**/yarn.lock') }}
-          restore-keys: |
-            ${{ runner.os }}-yarn-
       - run: yarn install --immutable
       - name: Turbo Cache
         id: turbo-cache
@@ -51,18 +43,10 @@ jobs:
       - uses: actions/setup-node@v4
         with:
           node-version: 18
+          cache: yarn
       - uses: oven-sh/setup-bun@v2
         with:
           bun-version: '1.1.42'
-      - name: Get yarn cache directory path
-        id: yarn-cache-dir-path
-        run: echo "dir=$(yarn config get cacheFolder)" >> $GITHUB_OUTPUT
-      - uses: actions/cache@v4
-        with:
-          path: ${{ steps.yarn-cache-dir-path.outputs.dir }}
-          key: ${{ runner.os }}-yarn-${{ hashFiles('**/yarn.lock') }}
-          restore-keys: |
-            ${{ runner.os }}-yarn-
       - run: yarn install --immutable
       - name: Turbo Cache
         id: turbo-cache