Using Github cache action to store packages to speed up action run times

Question

I have set up a GitHub action to run the rcmdcheck::rcmdcheck(args = "--no-manual", error_on = "error") function on my R package every time there is a pull request, but it's taking over 15 minutes each time to download and install all of the packages, then it needs to run through the unit tests, which are also taking a while to finish.

So, I want to try and cache the required packages and dependencies using the GitHub cache action. However, I can't figure out what needs to change from the R example provided.

Here is the github action yaml which I want to cache my dependencies on:

name: R

on:
  push:
    branches: [ "main", "dev" ]
  pull_request:
    branches: [ "main", "dev" ]

permissions:
  contents: read

jobs:
  build:
    runs-on: macos-latest
    strategy:
      matrix:
        r-version: ['4.1.1']
    env:
      GITHUB_PAT: ${{secrets.REPO_KEY}}
    steps:
      - uses: actions/checkout@v3
      - name: Set up R ${{ matrix.r-version }}
        uses: r-lib/actions/setup-r@f57f1301a053485946083d7a45022b278929a78a
        with:
          r-version: ${{ matrix.r-version }}
      - name: Install dependencies
        run: |
          install.packages(c("remotes", "rcmdcheck"), type = "binary", dependencies = TRUE)
          remotes::install_deps(dependencies = TRUE, type = "binary")
        shell: Rscript {0}
        
      - name: Check
        run: rcmdcheck::rcmdcheck(args = "--no-manual", error_on = "error")
        shell: Rscript {0}

The idea is that once the code is run for the first time, so long as none of the required packages, dependencies or OS changes, then it can re-use the dependencies from last time and skip a costly part of the run time.

**Further information:** The repository this runs on is private, and requires some packages which aren't on CRAN, which adds further complexity. Some are other private repo's and the other is stored here https://inla.r-inla-download.org/R/stable/src/contrib/INLA_21.02.23.tar.gz

I have tried to use the setup-r-dependencies functionality for this, and while it works just fine on another package, it doesn't seem to work for this package. (We were unable to resolve this despite posting a bounty, see my previous post)