DAL/Tests: simplify test

What

The test new attester attests, introduced in !13955 (merged) (see also !13900 (merged) for the context), is flaky. This MR should eliminate the flakiness.

How

Simplify the test by publishing only at the required level

More importantly, also wait for the connection between the producer and attester at the right level, and also wait for the attester to receive its shards. This should eliminate one source of flakiness, where if the connection does not happen at the right level or the shards are not received in time, so the slot cannot be attested.