Thanks for your reply, @cderv!
I tried (today's) daily version: The problem persists but using the tinytex option solves the issue. (I was not aware that tinytex can be "enabled" for RStudio without changing PATH system-wide, as it's the case with tinytex::install_tinytex().)
Interestingly, in the stable version of RStudio enabling the tinytex option seems to have no effect. Even the output remains "Running pdflatex.exe on test.tex...failed" instead of "Compiling document with tinytex ... completed" as printed by the daily build.