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()
There might be an error dialog or two about luatex.dll during the installation (like this), but that does not seem to hurt, and I just clicked “OK”. The installation directory is %APPDATA%/TinyTeX , where APPDATA is an environment variable that typically points to the path C:\Users\Your Name\AppData\Roaming .
So that error shouldn't be the cause of your problem. Is the installation in the AppData folder?
tinytex::tlmgr_path()
tlmgr path add
Use of uninitialized value in bitwise or (|) at C:\Users\201101~1\AppData\Roaming\TinyTeX\texmf-dist\scripts\texlive\tlmgr.pl line 1482.