It's not the full SV40 virus. It is an SV40 "promoter" placed on the DNA plasmid used to code for the mRNA of the spike protein and antibiotic resistance to kanamycin and another common antibiotic needed to separate successfully transfected E. coli from non-transfected organisms. Find Kevin McKernan on Twitter/X for the plasmid details. The COVID vaccines are contaminated with about a TRILLION DNA plasmids per injection due to sloppy manufacturing process. Another researcher, Phillip J. Buckaults, PhD, has replicated the DNA contamination findings from McKernan. Buckhaults is also on Twitter/X where his findings are referenced. Additional credit is due to JikkyLeaks on X/Twitter for early detection of contamination that McKernan refined.
The SV40 promoter helps drag the genetic "products" into the target cell nucleus.
The DNA plasmids weren't picked up in the manufacturing process, they were inserted intentionally.
If they were picked up in the manufacturing process, they would show up in other medical products manufactured with the same equipment.