Pull request #799 moved the DNS check to be the first thing we do as part of the connectivity tests. The rationale is that DNS is often the first thing to fail in subsequent connectivity tests, so best to highlight it at the beginning if it's broken.

However, if only connectivity across nodes is broken, the DNS check might pass because the backend DNS pod we use is located on the same node as the client. Hence, it will pass in one run and fail in the second, adding randomness to our CI and anywhere else we'd use the connectivity tests. Instead, we should check:

• That DNS resolution works with the local DNS backend (hence, basic local connectivity works).
• That DNS resolution works with the remote DNS backend (hence cross-node connectivity works).
• That DNS resolution works with the service (as done today, hence basic service plugging works).