Low furniture would not need as much screening at least while seated. Something like this would allow you to stretch your legs without an ottoman taking up space.

This has a small footprint with a flat seat that could double as a side table or plant stand.

How about a table and chairs with an umbrella and some large exotic plants elevated on a plant stand so that you have some privacy?

A privacy screen could get blown down by wind. Reconsider using plants in heavy pots instead. They need to be bushy at eye level.

Edited to add: the post by ratherbesewing shows a great illustration.

You could screen in your railings pretty easy. Bamboo screening/fence or outdoor worthy fabrics would probably be the easiest and least expensive. More pricey, but you could get outdoor privacy screens and attach those to the railings if you wanted a person height screen. Or there are kinds that have planter box bases that wouldn't require attachment- but footprint and weight considerations to consider. And you did say you didn't want plants so not sure if you would want planter boxes.

And something to consider. If this is a rental or HOA situation, you might need to check with them to see what is or is not allowed on your balcony before doing any more planning.

screening will make your porch claustrophobic and your apartment dark. With a trellis in a planter or plants in pots (they can be your indoor plants enjoying the summer outside) you can place them where there's a view you want to block.

If it's just one neighboring balcony, which does not appear to have any furniture on it, you can orient your furniture to face away. Because if there's no furniture, the neighbors don't use their balcony much.

I see you have a bug zapper. They are very effective at zapping all sorts of bugs, like pollinators and luna moths, but they are not effective at zapping mosquitoes, which is usually why people have them.

Best mosquito repellant is a fan on a low speed, they are weak flyers

Check condo rules and regulations before you do anything.

You might try a small sofa, or two chairs, a side table, and some plants. Below are a few different patio designs of ours which we thought might help you with your dilemma.

Palm Beach Polo Club · More Info

Modern Nantucket Nautical · More Info

Simply High Line · More Info

We offer some simple chairs or tables that would go well in the space. Some images are below. It is tough to see how big the space is exactly, but we are offering a new deep seating line that would also be nice on your balcony. Search Highwood USA on Houzz for more!

Highwood USA Conversation Tables · More Info

Highwood Adirondack Chairs · More Info