Well, what you describe with
all of our katas are performed against an opponent/s
sounds alot like the "step sparring" we employ(korean name escapes me at the moment), technically you can call these poomsae/katas aswell. Set routines you employ vs a partner.
Like this demo by my grandmaster, still consider him that even after I left tkd:
The concept of poomsae is,well,hard to explain. Yes, its a collection of techniques and you practice skill,transitions etc. But its also a form of shadow fighting. You dont just perform the movements, you are meant to visualize an opponent with every strike, every movement is offensive/defensive. Its also a way of incorporating techniques you rarely get to practice, by imagining an opponent.
To have a good poomsae you must understand it, understand the movements and principles behind it

Not only a philosophical pattern, for example, notice that the techniques in a poomsae does not really fit with what people consider tkd fighting. In a pomsae it takes the practical path, kick the kne,attack the groin,attack the throat etc.
Have to add though, that people who practice poomsae for demos often(in my opinion)lack something, its basically going through the motions..And you can actually get failed by masters(usually korean ones, they are extremely strict on form) for lacking emotion when performing it.