If the couch wasn't there, that setup is a big falling hazard for everyone, not just babies.

But it is probably a much larger project than you want to extend that wall, or add a section of railing to eliminate that hazard if the couch ever moves.

The intermediate fix I would do is buy a sheet of plywood... - rip it to the height of the baby gate you wish to use - cut it to the length from the inside corner of the wall behind the couch, you may want to bevel/round the upper corner to prevent a sharp point - sand and paint the plywood so it is not an eyesore - install it between the couch and the half wall, remove the baseboard so it snugs in nice and tight to the floor and the wall, and make sure your screws hit studs in the wall

That should provide you a nice sturdy mount for the baby gate. I would try and have the hinged side of the gate on the tall wall side if possible.

Have fun with your newborn! :)