I did some research on the item posted by the OP and traced it back to an outlet called "The People's Voice" which is a fake news site spewing misinformation.

For further information on self replicating or self-amplifying mRNA components visit the following:
https://pmc.ncbi.nlm.nih.gov/articles/PMC10266560/

https://www.medscape.com/viewarticle/self-replicating-mrna-vaccine-covid-prevention-2024a1000n53?form=fpf

There is no mention of the effects of these vaccines being able to spread from person to person as far as COVID vaccines are concerned, but that does not mean that there might not be attempts to develop such vaccines in the future but I did find an item reporting scientists attempting to develop self-spreading vaccines of other types and though they may not be COVID vaccines, I still don't like the sound of the methods they are using.
https://www.thegatewaypundit.com/2022/03/scientists-currently-developing-controversial-contagious-vaccines-can-spread-vaccinated-unvac