While, by default, the pdf engine used for rendering Quarto PDFs is xelatex, compliant with the fontspec package, it's totally feasible to change the Quarto engine to pdflatex (and I actually have to do so, related to a bad formatting of a maths symbol unrelated to flextable).

However, with the following lines:

you're assuming the default, when using quarto, is always fontspec compliant, generating errors when loading flextable within a Quarto framework whose metadata latex-engine key is pdflatex.