To help catch javadoc errors upstream, implement a downstream check on the generator similar to this one: googleapis/java-shared-config#662 that checks javadoc generation on a couple of libraries to ensure javadoc generation works.

In terms of what the javadoc generation should test for:

1. The current cloud RAD generation uses Java11 with this doclet: https://github.com/googleapis/java-docfx-doclet/tree/main/third_party.

2. In general, to account for self-service clients, the plain mvn javadoc:aggregate command should also pass. This should be checked on Java 17, and possibly Java 11 as well. If we migrate the cloud RAD generation to use Java17, then I think we don't need to check for Java11 anymore, but that will be a separate project.