Decouple codecov upload from coverage testing (#5534)

Do no repeat the whole coverage testing if the codecov upload fails.

### TODO

- [ ] Copy these changes to contrib if this merges

.github/workflows/ci.yml

@@ -5,8 +5,6 @@ on:
       - main
   pull_request:
 env:
-  # Path to where test results will be saved.
-  TEST_RESULTS: /tmp/test-results
   # Default version of Go to use by CI workflows. This should be the latest
   # release of Go; developers likely use the latest release in development and
   # we want to catch any bugs (e.g. lint errors, race detection) with this
@@ -95,24 +93,27 @@ jobs:
           check-latest: true
           cache-dependency-path: "**/go.sum"
       - name: Run coverage tests
-        run: |
-          make test-coverage
-          mkdir $TEST_RESULTS
-          cp coverage.out $TEST_RESULTS
-          cp coverage.txt $TEST_RESULTS
-          cp coverage.html $TEST_RESULTS
+        run: make test-coverage
+      - name: Store coverage test output
+        uses: actions/upload-artifact@v4
+        with:
+          name: coverage-artifacts-${{ env.DEFAULT_GO_VERSION }}
+          path: coverage.txt
+
+  codecov:
+    runs-on: ubuntu-latest
+    needs: [test-coverage]
+    steps:
+      - uses: actions/download-artifact@v4
+        with:
+          pattern: coverage-artifacts-${{ env.DEFAULT_GO_VERSION }}
       - name: Upload coverage report
         uses: codecov/codecov-action@v4.5.0
         env:
           CODECOV_TOKEN: ${{ secrets.CODECOV_TOKEN }}
         with:
           file: ./coverage.txt
           verbose: true
-      - name: Store coverage test output
-        uses: actions/upload-artifact@v4
-        with:
-          name: opentelemetry-go-test-output
-          path: ${{ env.TEST_RESULTS }}
 
   compatibility-test:
     strategy: