rptest: expose health check reason

[travisdowns]

If our health check fails, expose the reason in the exception message.

Also, downgrade the logging on the success path of the health check to info from warning.

Backports Required

• none - not a bug fix
• none - this is a backport
• none - issue does not exist in previous branches
• none - papercut/not impactful enough to backport
• v23.3.x
• v23.2.x
• v23.1.x

Release Notes

• none

[vbotbuildovich]

new failures in https://buildkite.com/redpanda/redpanda/builds/43977#018d234e-5e5c-42ff-91b7-3ab9937ec567:

"rptest.tests.random_node_operations_test.RandomNodeOperationsTest.test_node_operations.enable_failures=True.num_to_upgrade=0.with_tiered_storage=True"