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Describe the bug
setup-r-dependencies uses pak::lockfile_create() with no lib-parameter. Therefor it defaults to .Library which means only installed base packages are being detected and all (pre-)installed site-packages (.Library.site) are being ignored and will be reinstalled.
See:

To Reproduce
We're using nightly built base images for Github actions with most used R packages already included so we can speed up the install dependencies step in our workflows. As caching is being stored on the runner and not on the base image itself, it's not being used unless you rerun the same workflow/branch. Initial runs don't have cache but the installed site-packages should be checked, this does not happen because of the mentioned finding (.Library only contains R base packages).

Continuous-Integration:
    runs-on: ubuntu-latest
    container:
      image: ***.dkr.ecr.eu-central-1.amazonaws.com/base-images/builder-r-latest:latest

Expected behavior
Installed site-packages should be checked, this does not happen because of the mentioned finding (.Library only contains R base packages). Therefor all site-packages will be downloaded from remote repositories like CRAN or RSPM

Additional context
Possible workaround is to install the extra packages in the base images in the .Library folder (in our case it's /usr/local/lib/R/library) instead of the .Library.site folder (/usr/local/lib/R/site-library).
A nicer solution is to specify .Library.site for the lib-parameter of the pak::lockfile_create() call here, like so:

pak::lockfile_create(
  c(deps, extra_deps),
  lockfile = ".github/pkg.lock",
  lib = .Library.site,
  upgrade = (${{ inputs.upgrade }}),
  dependencies = c(needs, (${{ inputs.dependencies }}))
)

relevant (tried) env-variables:
R_LIBS_USER="/usr/local/lib/R/site-library"
R_LIBS_SITE="/usr/local/lib/R/site-library"
R_LIB_FOR_PAK="/usr/local/lib/R/site-library"