Update ruby-core workflow to just generate documentation

Since RDoc is now a bundled gem, we don't need to run test with Ruby core
with it commit by commit. But it'd still be beneficial to generate
documentation with the current RDoc commit and the Ruby master branch.

So this PR updates the Ruby core workflow to just do that.

.github/workflows/ruby-core.yml

@@ -15,7 +15,7 @@ permissions: # added using https://github.com/step-security/secure-workflows
 
 jobs:
   ruby_core:
-    name: RDoc under a ruby-core setup
+    name: Generate ruby/ruby documentation with the current RDoc commit
     runs-on: ubuntu-20.04
     strategy:
       fail-fast: false
@@ -50,13 +50,10 @@ jobs:
       - uses: actions/checkout@b4ffde65f46336ab88eb53be808477a3936bae11 # v3.1.0
         with:
           path: ruby/rdoc
-      - name: Sync tools
+      - name: Install RDoc locally
         run: |
-          ruby tool/sync_default_gems.rb rdoc
-        working-directory: ruby/ruby
-      - name: Test RDoc
-        run: make -j2 -s test-all TESTS="rdoc --no-retry"
-        working-directory: ruby/ruby
+          gem build rdoc
+          gem install *.gem
       - name: Generate Documentation with RDoc
         run: make html
         working-directory: ruby/ruby