It's difficult to tell from your one photograph, but most likely you could put full height walls up where the railings are now, plus a door to the hallway.........It won't require any structural additions and should be fairly reasonable..........

If sound is an issue, you should consider using 5/8" drywall and insulating between the wood framing. Also, the door that you add should be a solid core door rather than hollow core.

Ask several local contractors for a price and go from there.

If you put walls instead of the railing.....how would it look from down below? I am not sure I would like the high enclosed space. Is there another room you can put the office in and use this room for a sitting room ... using earphones to listen to music or read?

Really how much traffic do you honestly have that makes a home office not work IMO can’t be any worse than the noise in an actual office . What would you do with it if it were enclosed?

I'd install a murphy bed and then make that the guest bedroom for people I don't want staying too long.

The "value" of that balcony is being reflected in your insurance premiums and property taxes -- and, since heat rises) probably your heat/ac bills (which, to me, makes it surprising that your overhead light fixture for this space is not a centered ceiling fan and there is no obvious "return" for the heat/ac system visible in this space.).

Before you decide to close it off (potentially taking resale value off your home), know what is involved in making that change and what you'll end up with if you do.

Is this the only upstairs room or just an extended part of the hall or landing that leads to other upstairs rooms.

Were the balcony and patio doors built to enable the home to meet some local building code (such as fire escape requirement) -- would removing the balcony or doors or closing off the room create a problem with code compliance.

What heat/ac vents/returns are in this space; how will this effect the operation of and efficiency of your system.

How much -- positive/negative -- effect does the light entering via these patio doors have on either the stairs (if they lead to other upstairs rooms, too) and/or on the room below.

Do the stairs lead anywhere else; and, if not, and you decided to close this space off as an attic space, how much more remodeling would need to be done to where the steps and rail are now located if they were to be removed -- including, if applicable, covering up any steps beneath them that might go down to a basement.

What would closing this space do to the look of your ceiling.

If you decide to enclose this space, and, if doing so would not create code compliance or heat/ac problems, then, instead of building actual walls, you might consider leaving all of what you have in place to protect the resale value of your home and only adding floor to ceiling cabinets/shelving units (doors, glass or solid, optional) (with solid backs painted the same color as your walls or ceiling) placed just "behind" the railings.

For safety sake, you'd probably need to attach such storage units to the floor and/or ceiling and/or wall but that could do much less to decrease the value of your home than ripping out the original design.

You could even add a door frame between the units where the entry space is now located.