I have a lovely horse who was like this at first (when green). An unraced TB, super talented, but dead to the leg, and doing the minimum. He was exhausting to ride for me. He woke up, eventually, and is no longer like this. So it’s possible! LOL.
He was also stiff to ride, bending and softening was an issue, and much stiffer in one direction, no unsoundness issues. It all came better in time. Suppling exercises, grids, and carry a stick to back up your leg cues. Don’t accept a response that is not sufficient. Get the response you want in your ground work, on the lunge or in a big round pen. It’s a respect issue. If he respects you, he will pay attention to you. If he doesn’t respect you, he won’t move for you or pay enough attention to you. If he does not respect you, he will ignore you though he allows you to sit on his back. This is not riding, it is sitting on his back. Big difference.
When riding, go for a gallop somewhere where you have room to get his engine running. You are lacking the first step of the training pyramid, “free FORWARD relaxed motion”. Tense horses are missing the “relaxed” part of this step, you are missing the “forward” part. Look for “cue”, and the response you want, “forward”. And indicate to him when his response is satisfactory, a word, a pat on the neck.
When “the penny drops”, you are sitting on a different horse.