You are essentially correct, but since viruses mutate I took the choice to possibly supplement what I believed was my then current level of Covid immunity by getting two shots of Moderna vaccine and refraining from immune suppressing drugs for about ten day after my jabs.
The scientific understanding of Covid immunity is rather weak - so I gambled on the Moderna vaccine.
Both immune systems and Covid vary over time. The science of Covid control isn’t set in stone.
Good Luck to you.
Hope you made the right choice.