Fix publishing due to npm 7 bug (#3846)

eng/pipelines/templates/build.yaml

@@ -6,7 +6,7 @@ steps:
     displayName: "Install Node.js"
 
   - script: |
-      npm install -g npm
+      npm install -g npm@6 # Seems to be an with npm 7 and publishing https://github.com/npm/cli/issues/2624.
       npx @microsoft/rush install
     displayName: "Install dependencies"
 

rush.json

@@ -1,7 +1,7 @@
 {
   "$schema": "https://developer.microsoft.com/json-schemas/rush/v5/rush.schema.json",
-  "rushVersion": "5.35.2",
+  "rushVersion": "5.38.0",
-  "pnpmVersion": "5.13.5",
+  "pnpmVersion": "5.16.0",
   "pnpmOptions": {},
   "nodeSupportedVersionRange": ">=8.9.4 <15.0.0",
   // Disabling this during migration of other repos as it is causing issues.