What you describe sounds like executive dysfunction, which is just the name for when you want to do something but your brain and body can't muster up the energy and motivation to do it. It's exceedingly common for people with a range of mental illnesses. Your brain is utilizing most (or all) of its energy battling anxiety, depression, ennui, or whatever emotion(s) are negatively impacting you, so you don't have the energy left to do the things you actually enjoy because your brain is craving rest.
Like others have said, moving your body might help. Even if all it is is forcing yourself to stand up and walk across the room, it's better than staying sedentary for too long. Making sure you're drinking some water and getting some nutrients is also helpful. But those are just general tips for feeling better overall.
When I feel too overwhelmed to do something I enjoy, I try to ween myself onto it with smaller activities that are somewhat adjacent to my desired end goal. Like, if I want to play video games but am having issues getting off my phone, I try some phone games. There's plenty of puzzle games that work your mind and entertain you, but I also enjoy more games like Crossy Road or BitLife that require no real brain power. I use those games as stepping stones into the actual game I want to play, or I use them when I take a break from the video game to give my brain some rest.
As for the inability to relax, when I'm trying to recharge, I have very specific conditions. I need to be alone, I need my attention fully engaged (meaning I usually have music/a podcast/a video playing on my phone as I do something else), and I need to physically relax myself. For me, that means I need to exercise, but for you, that might be stretching, dancing, walking, massaging sore points on your neck/shoulders/back, rubbing your arms/shoulders/legs, stimming, playing with a fidget toy, or even meditation/mindfulness. Sometimes I have to do breathing exercises and talk to myself out loud just to bring my brain down to a less emotionally volatile place. It's dependent on the person, but I find that physical stimulation that either 1. exerts your anxious energy or 2. mediates it with soothing sensations makes relaxation a little easier.
Just remember that your brain is working overtime to deal with errant thoughts/emotions while still juggling everyday life. There is so much information coming at you nowadays that even the healthy brain gets burnt out after too long, so if you're dealing with mental illness or being neurodivergent, you've got even bigger hurdles to jump. Give yourself plenty of grace, understanding, and forgiveness. If you need more tips, I would suggest looking up methods to help with executive dysfunction. I can't vouch for any one trick, but you might find something useful.