webshot2 is meant to be a replacement for webshot, except that instead of using PhantomJS, it uses headless Chrome via the Chromote package.
# CRAN
install.packages("webshot2")
# Development
remotes::install_github("rstudio/webshot2")
You also need to have the Chrome browser installed on your system. You can also use other browsers based on Chromium, such as Chromium itself, Edge, Vivaldi, Brave, or Opera.