The process works in that a complete PDF is produced in the _book directory, but it then runs again to generate a PDF in the top directory. This second process fails because TeX/LaTeX packages included via preamble.tex are not included.
generates the file in _book only, but the Rstudio Build button tries to build a second version in the parent directory. As can be seen from the log it actually uses a different command (far fewer arguments).
Must be an Rstudio peculiarity (it did not previously do this).
Yes this is fairly standard. I am not sure to understand what could happen here. I don't recall RStudio is doing something specific
If it is working with Command Line, I think this is then an RStudio issue that should be reported to their github repo. I don't know exactly what build book is doing.
One idea though
You got this in your index file, so you are asking to render the index.Rmd to pdf_document explicitely.
It is possible than building with RStudio renders all the formats ! including this one.