Sets up the test targets for integration tests with the new rule.
The targets will match the configuration of the previous integration
test setup (through the dictionary in a `bzl` file).
Note: We already add `setup_chromium` based on whether Chromium tests
run as part of this integration test. In a follow-up commit we can then
remove puppeteer and rely on the Bazel-managed version of Chromium.
PR Close#44238
