>So from my layman understanding, the immunity should be more resistant to a mutation of the spike protein.
There have been several studies that suggest vaccination provides stronger immunity to mutations. Here's one titled Vaccine-induced immunity provides more robust heterotypic immunity than natural infection to emerging SARS-CoV-2 variants of concern:
Did any of these studies compare people who were vaccinated with people who had COVID19 at the same time relative to sampling? In this paper the two groups are separated in time, making it very hard to interpret the results. The effect could simply be due to difference in antibody titer at different times from infection.
There have been several studies that suggest vaccination provides stronger immunity to mutations. Here's one titled Vaccine-induced immunity provides more robust heterotypic immunity than natural infection to emerging SARS-CoV-2 variants of concern:
https://www.researchsquare.com/article/rs-226857/v1