What are we searching for with our awareness? It can't be complete knowledge or absolute articulation, as even an intelligence vastly superior to ours might struggle to amass such data and even an apparatus with vastly more artifices would struggle to articulate it. Are we just searching for the equivalent of a witty anecdote or something in the grand scheme of things?

It depends.

If the intelligence is external to the universe, then yes. Otherwise, finite / infinite nature not withstanding, the universe is a closed set from the point of view of any member of the set. The minimum set containing all knowledge pertaining to the universe, is the universe itself. So, it's impossible to know all knowledge and be part of the universe at the same time since this effectively splits the universe into two subsets: you and all knowledge including you. It's self-referential and a paradox.

As for the lesser minds, no, all knowledge can't be transmitted for the same reason. We are part of the closed set and can't create subsets which increase the size of the original set.

But what if there is nothing external to the universe, that means that strictly speaking, the universe can never be fully understood. So what's the point in amassing eternally incomplete knowledge? Except for having the odd witty anecdote (reality).

Because we can't understand the universe as a whole, we can never amass all causal information. Since the universe is dynamic, our incomplete causal knowledge means we'll never fully understand the future. So, we can never exhaust the unknown, anyhow. There will always be something new to learn. I believe, no intelligence could comprehend the total sum of all the universe is for one would have to be the universe itself.