There is no objective answer to your question.
The Academy tends to attract more locals than tourists, so based on that, i might be a bit more conservative.
But, as you said, it's students. So, I ask if your son or daughter had fought to get into the academy and was now show casing her/his talent in a venue as beautiful and prestigious as the Grand Hall, how would you dress to see her?
If you suspect the audience includes proud Hungarian parents, how would you imagine that they would dress for their children?
How about the students? What might they be expecting?
Assuming you feel as a guest in their home and you want to be seen showing the utmost respect, how would you dress? Is the bar higher since you are somewhat uninvited inserting yourself into their event?
Then mama always said that it's impossible to overdress, but the opposite isn't true.
I can only say what I would do. I have a pair of travel slacks that weigh a fraction of that of a pair of jeans and are never out of place. They pack better than most any jean or chino so packing is not an excuse for me. The shirt in the summer can be a polo ot even a really slick crew neck. In the winter a sweater. Again, no impact on packing. The jacket is a travel blazer that I wear on the plane. Full of great pockets for phone, passport, tickets, etc. It's my travel vest. I wore it to Bosnia & Herzegoivnia last week. Glad I did, for one special evening.
I'm still not sold on the report on the Opera. The last time I was there was 3 years ago, and because of a similar thread at the time I made a mental note of what I saw and it wasn't what the OP experienced. But things might have changed in 3 years. I am also left uncertain because the OP said everyone around him was a tourist .... so I presume that was the situation in general. Tourist choices don't necessarily reflect local cultural values. But I could be dead wrong in my assumptions. But I've been lazy. I could settle it in my mind by just walking past either venue 30 min before show time. I would do that tonight, but Zoltan just poured a nice white Kadarka.
If you are looking for something more concrete, read the Opera's recommendations in their FAQ and comply. The Academy is at least as .... pick a word. Or Google the venue and look at photos of how people are dressed.
So, my advice is think it through and choose in a manner that will provide a ceartinity that you will feel comfortable in both your style and in your demonstration of your respect to the ocassion, the performers, the venue, and the others there that night. And you might end up "over dressed" (there really is no such state).
If i seem overly conservative in my own actions, I confess to having a very deep seated need to avoid offending the locals of my host country. Few things I take more seriously.
Stop it at 22 seconds to see the audiance: https://youtu.be/vzXXQU23SDQ?si=XN28PjoIzDQFudIZ
Kenko mentioned the Mupa. Depends. The venue does everything from children shows to rock, to jazz to classical; and evening to matinee so a random one off experience may or may not be .... but its a start.