Here is a read about the spike proteins they are not produced as you say you need to understand how different vaccines work.
https://www.chop.edu/centers-programs/vaccine-education-center/video/what-stops-body-continuing-produce-covid-19-spike-protein-after-getting-mrna-vaccine
https://www.nytimes.com/interactive/2020/health/oxford-astrazeneca-covid-19-vaccine.html
