Similar experience with a similar medication but not Kevzara. I was on Actemra which is another IL-6 inhibitor similar to Kevzara.

When Actemra was started for PMR, I tapered rapidly down to 3 mg. At one stage I tapered by 1 mg per week while taking Actemra. When I reached 3 mg of Prednisone, I felt awful. The extreme fatigue you mentioned was overwhelming. I also had scattered aches and pains that felt like PMR was returning. The episodes of dizziness were what I remember the most because I had to hang on to things thinking I was going to black out and fall.

My symptoms were consistent with adrenal insufficiency. My cortisol level was too low to allow me to taper my Prednisone dose any lower than 3 mg.

Adrenal insufficiency is another barrier to tapering off prednisone. Adrenal insufficiency gets complicated but the following is good guidance about the subject. The first paragraph explains what happens and it isn't because of Kevzara or Actemra. It is what happens when we take corticosteroids like Prednisone for more than a few weeks. It is easy to confuse symptoms of adrenal insufficiency with a PMR relapse.
https://academic.oup.com/ejendo/article/190/5/G25/7663654
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I was on Prednisone for 12 years for PMR. My symptoms of adrenal insufficiency persisted for a long time but things gradually improved. I had to stay on 3 mg of Prednisone until my cortisol level improved. Eventually I was able to successfully taper off Prednisone