https://www.scientificamerican.com/article/what-we-know-so-far-about-how-covid-affects-the-nervous-system/

Many of the symptoms experienced by people infected with SARS-CoV-2 involve the nervous system. Patients complain of headaches, muscle and joint pain, fatigue and “brain fog,” or loss of taste and smell—all of which can last from weeks to months after infection. In severe cases, COVID-19 can also lead to encephalitis or stroke. The virus has undeniable neurological effects. But the way it actually affects nerve cells still remains a bit of a mystery. Can immune system activation alone produce symptoms? Or does the novel coronavirus directly attack the nervous system?

Some studies—including a recent preprint paper examining mouse and human brain tissue—show evidence that SARS-CoV-2 can get into nerve cells and the brain. The question remains as to whether it does so routinely or only in the most severe cases. Once the immune system kicks into overdrive, the effects can be far-ranging, even leading immune cells to invade the brain, where they can wreak havoc.