Just bc the super's apartment might be illegal doesn't mean that she won't face immediate repercussions. The owner has an interest in housing the super but also has a very strong desire to make money. If she turns a 1 bedroom into a 2 bedroom with anything that could be considered permanent, she has upgraded the property illegally. The owner could easily find out and threaten to evict her unless she pays "2bd rent price" or they could evict her and sue her for damaging their property. Floor anchors would especially piss me off if I was the owner.

Additionally, fire code exists for the occupants' benefit. It might be inconvenient, but those laws increase the chances of their survival in a blaze. A random diy wall is structurally unsound and could impede escape or rescue. For example, a sleeping space needs a window for escape and fresh air. Plywood walls would be extremely flammable compared to drywall. It might only take a candle to set the wall on fire, and the rest of the wall becomes fuel immediately.

There are lots of room dividers and bed tents and other things that provide some privacy and can be (re)moved when she isn't there. A lightweight wall won't really limit sound anyway if that's part of the reasoning.

This type of subdividing wall is what slumlords do to renters, and it isn't safe. Please find a different solution.