Stockwerkeigentümergemeinschaft is another very useful concept. Now that you brought it up I remember seeing this word in the official paperwork, but learning by heart such a monster takes some practice.
I think the general point is that you need to find out what all the levels or the rules are (the purpose of your opening question) and then abide by them
or else just take a chance, go ahead with your project, and then wait and see whether anyone else - who has read the rules - finds a legal way to object.
As a tenant , one faces the caretaker , the rental agency and the landlord . That's it. They, in turn, have to deal with the rules imposed by the owners' collective, and then by the municipality.
As an owner , as you are, one has to deal with the rules of owners' collective (of which each owner is automatically a member, has access to the agreed rulebook and can take influence to try to change the rules) and they in turn contract with a caretaker/agency. Both the collective and the caretaking agency can impose rules about balconies. And all of these rules are subject to those of the municipality .
If other people have screens up then it's pretty safe to assume the OP can have one too - though they ought to check if there are any rules regarding colour etc.
If no-one else does then:
It's either not allowed. It's allowed but within written parameters. It's allowed and anything goes. No-one cares. No one had discussed this before and a meeting will need to be held with other owners to discuss whether this can be allowed and if so, in what guise.*
*IME, the last one happens quite a lot, especially with a newer set of apartments.
Crucially, the property management company sometimes make the decision to decide this for you but that is not their job - their opinion does not matter.
You need agreement and consensus with other owners who may not agree with you.
Friends of ours currently have this discussion in their complex. The owners disagree with one another about where people are allowed to park their bicycles. The owners' collective's rules state that the property management decides about x, y, and z, etc., including, in this case, bicycle parking.
Many of the owners want to change that parking, but the property management says they'll do things according to their own rules, or else they're leaving. Some owners want to continue with this management company (because they're doing enough things right) and some want to ditch them (because the bicycle issue is the nth dispute). And so they're going round and round.
It probably depends on the size of the complex too. It would probably be impossible to reach a consensus amongst owners in a massive apartment complex.
Ours was much smaller so we had meetings to decide these things but generally people had been pretty fed up with an abundance of rules and regulations when they were tenants so everything was a bit more relaxed.
As the sayign goes "easier to apologize than ask permission".
If you keep asking around, you might end up raising attention to an otherwise non-issue. You don't need to be more catholic than the vatican.
FIY: Rules adopted by an owner's association are very often nont enforcable, in particular if these unduly restrict your exclusive right to use your share. A good example is forbidding barbequing. Lot of associations forbid it (or restrictict it to gas or electro - which is not barbequeing just buring of stuff) but the ban is mostly not enforcable.
OP however asks about the balcony, that's personal space. Nobody else has any say in this for what OP describes (just stay in the "airspace" of the balcony).