ci: migrate to bun as package manager

Signed-off-by: Vladislav Polyakov <polrk@ydb.tech>

Author: polRk

.github/actions/setup/action.yml

@@ -1,6 +1,6 @@
 name: Setup CI
 description: |
-  This action sets up Node.js and installs dependencies for the project.
+  This action sets up Node.js, Bun and installs dependencies for the project.
   It also configures caching for TurboRepo to speed up the build process.
 
 inputs:
@@ -15,9 +15,11 @@ runs:
     - name: Setup Node.js
       uses: actions/setup-node@v4
       with:
-        cache: 'npm'
         node-version: ${{ inputs.node-version }}
 
+    - name: Setup Bun
+      uses: oven-sh/setup-bun@v2
+
     - name: Setup turbo
       uses: actions/cache@v4
       with:
@@ -28,8 +30,8 @@ runs:
 
     - name: Install global dependencies
       shell: bash
-      run: npm i -g turbo prettier typescript @changesets/cli @arethetypeswrong/cli
+      run: bun i -g turbo prettier typescript @changesets/cli @arethetypeswrong/cli
 
     - name: Install dependencies
       shell: bash
-      run: npm ci
+      run: bun ci