Update GitHub Actions workflows. (#662)

This PR was automatically generated by the
update-workflows-single-bridged-provider workflow in the pulumi/ci-mgmt
repo, from commit 52b77e4c448dd747630cff0918ade69cef3b4f16.

.github/actions/setup-tools/action.yml

@@ -0,0 +1,38 @@
+name: Setup Tools
+description: Installs all tools (Go, Node, Python, .NET, Java, Pulumi, etc.) using mise
+
+inputs:
+  cache:
+    description: Enable caching
+    required: false
+    default: 'false'
+
+runs:
+  using: "composite"
+  steps:
+    - name: Setup mise
+      uses: jdx/mise-action@be3be2260bc02bc3fbf94c5e2fed8b7964baf074 # v3
+      with:
+        # Latest working version. See https://github.com/jdx/mise/discussions/6781
+        version: 2025.10.16
+        github_token: ${{ github.token }}
+        cache_key: "mise-{{platform}}-{{file_hash}}"
+        cache_save: ${{ inputs.cache }}
+
+    - name: Setup Go Cache
+      uses: actions/setup-go@d35c59abb061a4a6fb18e82ac0862c26744d6ab5 # v5.5.0
+      with:
+        cache: ${{ inputs.cache }}
+        cache-dependency-path: |
+          provider/*.sum
+          upstream/*.sum
+          sdk/go/*.sum
+          sdk/*.sum
+          *.sum
+
+    - name: Setup Node
+      uses: actions/setup-node@2028fbc5c25fe9cf00d9f06a71cc4710d4507903 # v6
+      with:
+        # we don't set node-version because we install with mise.
+        # this step is needed to setup npm auth
+        registry-url: https://registry.npmjs.org