It’s what Leebo said in essence, but personally, based on the difficulty I had parsing your sentence at first, I think I can make a case for the importance of making the purpose of で clear by adding は or by replacing it with a phrase that indicates that the context of discussion is being highlighted.
It could of course just be that it’s been a while since I’ve seen a sentence this long, but for some reason, I kept getting stuck around
I kept telling myself, ‘This is way too long. There’s no way that 問い is linking to 思っています, but I keep feeling like that’s what’s happening. What am I missing? Isn’t there another division somewhere?’ I eventually realised that the final verb of that chain of clauses was actually 探る, and that the entire chunk was modifying 意識. My suggestion would be that for the sake of clarity, you add という right after 探る so that the reader knows that the modifying phrase is something long, very possibly almost everything that has gone before. However, that’s probably not strictly necessary, and maybe my parsing isn’t as good as I think it is.
Nonetheless, here’s the thing: initially, I interpreted「学校のプロジェクトで」as a simple circumstantial element likely meaning ‘in a (certain) school project’, and proceeded to read the rest of the sentence as a series of actions undertaken during that project. I read it like a series of events in a story, and I had no idea why「が重要だと思っています」appeared because I thought 思っています was at the same level of the hierarchy as 傾け and 問い. (For a while, ‘thinking’ just seemed to fit better with ‘asking’ and ‘lending one’s ears’.) Even if I had parsed it correctly the first time around, it still felt wrong because as a series of events, everything from 傾け to 探る felt like something that would happen in isolation or that had already happened, so I couldn’t see why the ている form was being used: either 思っています was at the same level as 学校のプロジェクトで, which would make little sense unless you were at a project meeting and talking about it; or 学校のプロジェクトで was part of the relative clause that stretches all the way to 探る and modifies 意識, which makes more sense but is a little strange, because that makes it sound like there’s a specific sort of ‘awareness’ or ‘frame of mind’ that is characterised by being involved in a school project, and that this frame of mind is important (even though it’s not clear that it exists).
To round it all off, the interpretation that probably makes the most sense – and which I think is what you intended, right? – is the one that requires で to be on the same level as だ. Specifically, 重要だと思っています expresses a judgement, so it would be good for it to have a context, because few judgements are general or absolute. That’s why using では or においては is helpful, particularly the は itself: it makes it very clear that you’re making a judgement in this context. Without it, as I’ve just illustrated, there are too many possible ways placing of で into the hierarchy of the sentence. I believe that’s why you received such feedback, and I hope my explanation (along with my stories of faulty parsing) makes things clearer.