The following is the commands I used to get tinytex installed. Does this follow what you also did?
install.packages('tinytex')
# Install tinytext
tinytex::install_tinytex(force = TRUE)
# Printout session info for tinytex
xfun::session_info('tinytex')
# Execute the tlmgr command to search for LaTeX packages,
# install packages, update packages, and so on.
tinytex::tlmgr_path()