Thanks a lot for this useful advice.
I was able to manage now the package installation using github action.
The vignettes of my package require additional tex style sheets. Which in rstudio I do add by using:
> tinytex::parse_install( text = "! LaTeX Error: File `ctable.sty' not found.")
tlmgr search --file --global "/ctable.sty"
tlmgr install ctable
I have tried to find other projects that also have vignettes and github actions but I was unable to find these.
Any idea on how to add these style sheets in Github actions?