This particular paper has flaws - as you mentioned, only a very small number of peptides are measured. I work on proteomics, and I remember this discussion from when the paper was initially published: https://mstdn.social/@pwilmart@scicomm.xyz/11087205681645628...
Paleoproteomics isn't what I would call well developed at this stage. How do we know that the peptides that were detected were actually from Vlad? Many people may have handled the letters over the years.
The authors acknowledge that it's a possibility. But there are mitigating circumstances. From the article: "the Sibiu Archive was founded in 1465 and it has been officially operating since that year. So, the two well-preserved documents of 1475 immediately began to be stored in the city’s official archive."
[1] The authors seem to have gone to great length to verify that the letters were not contaminated. Among other things, they created and touched a modern letter, which they also analyzed. Remarkably only 20 peptides were in common between old and new.