I had severe Covid in Dec 2020 and again in Sept 2021. I have to say what came AFTER that first Covid infection was far worse than actual COVID.

I had that lack of balance, also heavy legs, would fall, etc.. I still have some balance issues but they are improving. I had a couple of periods where I had Vertigo. Never had that before in my 58 years and happy to say that also seems to have gone away. Thankfully, that was awful.

Physical Therapy might be helpful specific to the balance issues . I used a wheeled walker a few times and now still use a cane here and there on days I feel extra off balance.