Years ago I had prostatitis (non-bacterial) which gave me some of the symptoms you described, symptoms similar to what I've read about Long Covid. I felt at times like I was on an elevator moving up or down, off-axis, fatigued.
Today, I have a prostate size above a hundred and I have been with a catheter since Aug. 2022. To my knowledge, I did not test positive for Covid until 2023, it lasted 11 days. 11 days of symptoms that passed like individual train cars (I didn't receive the shots). Then I came down with it again, lasting only four days.
Going back to before I was catheterized, I didn't know that the urine had been backing up to my kidneys, because I thought I was voiding all my urine, frequently. I began to notice "some" of the symptoms described as Long Covid. Exercise intolerance. Sedentary, heart palpitations while walking, out of breath while walking, distended stomach at times, dizziness, vertigo-like sensations, elevated blood pressure, post exertion fatigue and general malaise. The ran an ultrasound and my kidneys and bladder were full of urine, a LOT of urine. The gave me a catheter and it all ran out. I was diagnosed with "Bi-lateral Hydronephrosis." It took a week or so to normalize and the symptoms went away.
Since I had covid for the second time, I have terrible insomnia, exercise intolerance, but no dizziness (I don't take any medications for hypertension or inhibitors to relax the bladder), post exertion fatigue and a situational depression that has gotten worse, amplifying these symptoms.
So, getting back to your question that compares Long Covid to Prostatitis symptoms, in my opinion, you have a large prostate with an inflammation that's not bacterial, if you've had Covid, irrespective of vaccination, or not, (there is also a study that came out about Long Vaccination) it could be related to covid if you've already had it, or it could be a complicated mix of prostatitis, L.C. and the possibility that you are not voiding. I suggest that you ask for a bladder / kidney ultrasound to rule out beginning hydronephrosis- this can cause permanent kidney damage which leads to a host of other symptoms. I'm glad you asked the question, I don't think you're coo-coo for coco-puffs, LC can exacerbate any pre-existing condition.