You need to ask your landlord.

Very doubtful a landlord would allow it. If they did would have to be a battery system, and it would be extremely foolish to take anything off-grid if you have commercial power avaialble as it will cost you around 20 times more for electricity. It would cost you $1500 cash to save you $1 or $2 on your monthly electric bill.

I worked for a property management company for years. I can tell you right now it would not be allowed. You would either have to alter the electrical wiring of the apartment for a grid tied system, or store batteries in your apartment for an off grid system. Neither of these would have flown at the apartments I worked at. Batteries are considered hazardous materials and you signed a lease that probably said that you agree not to store hazardous materials in your apartment. Your lease also states that if you alter the electrical wiring system and start a fire or cause any damage YOU are liable for all costs incurred. Read your lease agreement you'll see what I mean.

Not to mention that you as a tenant will never be able to get an interconnect agreement with POCO under those conditions and using a Plug-and-Pray inverter is just foolish as well as illegal.

You're right. I was not specific enough. Creating a cogeneration system (grid tie) of any kind would constitute alteration of the electric system of the apartment. That would be cause for eviction and make the tenant liable for any damages incurred.

The company I worked for was very strict. If we saw solar panels on your balcony, I would be sent to cut the wires and take them. They would consider them to be a fire hazard. You were not allowed to have any fire hazards on your balcony; grills, candles, tiki torches, lamps, wired lights. I'm sure solar panels would fall under the fire hazard category. Also no tenants were allowed to connect anything to the outside of the building without written permission, if you did it automaticly became the property owners property and we could take it. This included stuff like satellite dishes and flags and the like.

It's a long time later.

These days apartment residents COULD buy a camping or RV style battery/panel setup and use it on their porches.
Attaching to a railing however would likely trigger a response by the owner.
And there's no way this will ever save enough energy money to offset the cost, but it's possible.
These days all sorts of e-Bike e-Scooter and gaming laptop batteries of similar size are tolerated despite the risks.

California had a program called VNEM for solar credits to apply to apartment renters, but that will die as of 2/15/2024
unless an application is filed by the owner. After that's dead there are ways in some areas to invest $$$ into "community solar" and get paid for the solar earnings.