Chickenpox is a retrovirus, which is why it can linger in your body for decades, as it transcribes itself into selected portions of your genome to hide and then later re-emerge. SARS-CoV-2 is not a retrovirus.
Varicella-zoster virus (chickenpox/shingles), while it does create latent infections, is not a retrovirus. Retroviruses like HIV actually insert a copy of the viral genome into the host cell's DNA. VZV and other herpesviruses have a different latency mechanism[1] than retroviruses. SARS-CoV-2 probably does not cause latent infections, but could potentially cause a chronic infection similar to other RNA viruses like Hepatitis C. I would suspect it probably doesn't, but it is certainly possible.
How odd, this is not what I was taught decades back. I suppose I will have to refresh. This is like finding out that Mercury is not tidally locked to the Sun, despite that being in textbooks forever.
I must have been confused, or the presumed information source I remembered is much harder to find than expected.
The issue isn't the virus lingering, it's apparently blood clots throughout various organs, which can cause problems years after they come to be. A friend of my family died from unexpected bleeding/brain crushing after a small blood vessel in his brain popped. This was many months after the issue was first noticed, and a few months after one of to-be-two operations was done to prevent that clogged blood vessel from bursting due to over-pressure.
1: https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3118253/