docs: Update README

How would I render the README with minimal changes? My goal was to include the new-ish rchk runner. Also, should the `rhub_platforms()` function have an example that is run in pkgdown mode only (`Sys.getenv("IN_PKGDOWN")`)? Is asciicast actually used for animated images here, or only for coloring the output in the pkgdown? For the latter case, I'm now using a separate `index.md` that is created as a side effect of rendering `README.Rmd`, see, e.g., https://github.com/tidyverse/duckplyr/blob/main/README.Rmd#L21-L33.