I think if you are happy with the workflow/output you have there is no reason at all to change. w/r/t to websites and books we have put a lot of investment into features for both (https://quarto.org/docs/websites/, https://quarto.org/docs/books/). If you compare books with Bookdown vs. Quarto vs. JupyterBook I think you'll find that each does some things better than the others (so again if you are happy w/ your existing tools no reason to change).
Quarto is the next generation of R Markdown, so over time it will surpass R Markdown in features/capability (I think in most areas it already has). Note that Quarto will read and render existing Rmd files without modification, so when you decide to switch isn't a terribly big deal. You can use the monofont option to specify an alternate code font.
The idea is that we've separated running computations into pluggable "engines" (whereas in R Markdown everything was hard-coded to use R/Knitr). In Quarto we can use Knitr, or Jupyter, or Observable JS (and can add additional engines in the future). R Markdown was a tool created exclusively for R users whereas Quarto is for users of any language that want to create reproducible documents with Pandoc/markdown.
Yes, it's being created by the same group that created R Markdown / Bookdown. Similar concept but implemented in a cross-language fashion rather than being tied to R.
Hi there, member of Quarto team here. Quarto is actually being created by the same core group that created R Markdown. It's essentially the same idea but implemented in a cross-language fashion. I should also note that it is designed to be highly compatible w/ existing formats (you can render nearly all R Markdown documents as well as Jupyter Notebooks unmodified w/ Quarto).