DOL and OSHA, as well as other federal agencies, are working diligently to encourage COVID-19 vaccinations. OSHA does not wish to have any appearance of discouraging workers from receiving COVID-19 vaccination, and also does not wish to disincentivize employers' vaccination efforts. As a result, OSHA will not enforce 29 CFR 1904's recording requirements to require any employers to record worker side effects from COVID-19 vaccination at least through May 2022. We will reevaluate the agency’s position at that time to determine the best course of action moving forward.
https://www.osha.gov/coronavirus/faqs