So, my cat is about 3 years old. She was never really playful, she only really played with her toys for a day or two (longest was a week) before getting bored of them. I can only keep her in my room because of the "no pets" rule in my apartment complex. But she can roam around in there. All she does is sleep all day. She doesn't play with any toys anymore. When she wants to be held, she stays for about 10 seconds before wanting to be put back down. She doesn't like to play, or move around a lot. It could be because she is stuck in my room all the time, or part of her personality. But I'm not completely sure.
I remind you that cats have their own character, some are playful, some are lazy, others might just want to be pet when they want, other can't live without human interaction and so on.
You mention the cat has never been playful, and that could be an indicator of her character. A cat doesn't need to be playing 24/7 in order to be a happy cat. But you also mention you keep the cat locked in a room and that's a huge warning sign. Cats need open space to investigate, and feel like a "real" feline, or in its absence, high places.
Your cat might(vague assumption) be depressed from not receiving the right stimulation and the lethargic behavior could be a sign of it.
As I noted in my comment, such a small space can take a toll on an animal that by instinct wanders around the place it lives. I would recommend you to invest in kitty castles or DIY shelves where the cat can climb to; having a high place to view her somewhat-small kingdom could make a difference.