First, congratulations on all of those offers!
Q: If indeed I'd like to move to MBB, which company would give me the best chance in terms of reputation, but relevant work as well? (not sure if writing meeting minutes will be considered very relevant)
A: You alluded to this, but it's the one where you will have the most responsibility and rise up the fastest. I would much rather see some impressive bullet points under these experiences than I care about any of the brands. Furthermore, if I see you promoted a few times, that's a clear positive signal...so, figure out what exactly is expected from you at each of the firms AND what the opportunities are for moving upwards within them.
Would specialising this early in my career (i.e. choosing the energy-focused consulting) limit my opportunities long-term?
A: Yes, you do start to get funneled (like it or not) the moment you specialize. You can avoid this in some ways, but the path narrows over time.
Q: I know Hovarth is well-known in DACH, but unsure what reputation they have in the rest of Europe? Couldn't find much in terms of work quality, is it safe to assume they are similar to Tier 2 (ATK, RB) or they should be separated due to the focus on Controlling?
I personally don't know them but upon looking them up they appear to be borderline Tier 2, or perhaps in boutique territory.