Are you building the pkgdown website with the GitHub Actions from actions/examples at v2-branch · r-lib/actions · GitHub (that you might have gotten via GitHub Actions setup — github_actions • usethis)?
If so you can use the Config/Needs/website field in DESCRIPTION.
Here is an example, in pkgdown itself pkgdown/DESCRIPTION at 7fe9e802df2964d483d0267f1d5a59aa7b3c685d · r-lib/pkgdown · GitHub
Config/Needs/website: usethis, servr
The idea of custom fields is mentioned in the second edition of the R packages book R Packages (2e) - 10 DESCRIPTION and NAMESPACE