ci(.github): remove the go-cache action (#27250)

Closes https://github.com/coder/internal/issues/1619
Closes ENG-3039
Closes https://github.com/coder/internal/issues/1002
Closes ENG-3018

The `test-go-pg` Go cache grew until the post-job save could no longer
complete within the job timeout, cancelling the job on every `main` run.

Depot runners already provide remote Go build caching via
[`GOCACHEPROG`](https://depot.dev/docs/cache/integrations/gocache),
which writes every object it serves into `GOCACHE` and never evicts, so
persisting `GOCACHE` with `actions/cache` on top just carries an
ever-growing directory forward. #20510 removed the custom build cache
steps for exactly this reason, and the `go-cache` action introduced in
#25727 unintentionally reinstated them.

The action is now removed entirely, along with its module cache
persistence: a full cache miss plus cold `go mod download` on a Depot
runner takes about 10 seconds, faster than any warm `actions/cache`
restore of the module cache was.

`setup-go-paths` is kept, as it points `GOCACHE` and friends at the
Windows RAM disk, but its now-unused caching-related outputs are
removed.

.github/actions/go-cache/action.yml

@@ -1,76 +0,0 @@
-name: "Go cache"
-description: Restore and save Go build and module caches.
-inputs:
-  cache-path:
-    description: "Optional newline-delimited cache paths. Defaults to go env GOCACHE and GOMODCACHE."
-    required: false
-    default: ""
-  key-prefix:
-    description: "Prefix for the cache key."
-    required: false
-    default: "go"
-  download-modules:
-    description: "Whether to run go mod download after restoring cache."
-    required: false
-    default: "true"
-runs:
-  using: "composite"
-  steps:
-    - name: Compute Go cache key
-      id: go-cache
-      shell: bash
-      run: |
-        set -euo pipefail
-
-        if [[ -n "${INPUT_CACHE_PATH}" ]]; then
-          paths="${INPUT_CACHE_PATH}"
-        else
-          paths="$(printf '%s\n%s' "$(go env GOCACHE)" "$(go env GOMODCACHE)")"
-        fi
-
-        go_version="$(go env GOVERSION)"
-        paths_hash="$(printf '%s\n' "${paths}" | git hash-object --stdin)"
-        hash="$(
-          {
-            printf '%s\n' "${go_version}"
-            for file in go.mod go.sum; do
-              if [[ -f "${file}" ]]; then
-                git hash-object "${file}"
-              fi
-            done
-          } | git hash-object --stdin
-        )"
-
-        {
-          echo "path<<EOF"
-          echo "${paths}"
-          echo "EOF"
-          echo "key=${INPUT_KEY_PREFIX}-${RUNNER_OS}-${RUNNER_ARCH}-${paths_hash}-${hash}"
-          echo "restore-key=${INPUT_KEY_PREFIX}-${RUNNER_OS}-${RUNNER_ARCH}-${paths_hash}-"
-        } >> "$GITHUB_OUTPUT"
-      env:
-        INPUT_CACHE_PATH: ${{ inputs.cache-path }}
-        INPUT_KEY_PREFIX: ${{ inputs.key-prefix }}
-
-    - name: Restore Go cache, save on main
-      if: ${{ github.ref == 'refs/heads/main' }}
-      uses: actions/cache@27d5ce7f107fe9357f9df03efb73ab90386fccae # v5.0.5
-      with:
-        path: ${{ steps.go-cache.outputs.path }}
-        key: ${{ steps.go-cache.outputs.key }}
-        restore-keys: |
-          ${{ steps.go-cache.outputs.restore-key }}
-
-    - name: Restore Go cache read-only
-      if: ${{ github.ref != 'refs/heads/main' }}
-      uses: actions/cache/restore@27d5ce7f107fe9357f9df03efb73ab90386fccae # v5.0.5
-      with:
-        path: ${{ steps.go-cache.outputs.path }}
-        key: ${{ steps.go-cache.outputs.key }}
-        restore-keys: |
-          ${{ steps.go-cache.outputs.restore-key }}
-
-    - name: Download Go modules
-      if: ${{ inputs.download-modules == 'true' }}
-      shell: bash
-      run: ./.github/scripts/retry.sh -- go mod download -x

.github/actions/setup-go-paths/action.yml

@@ -1,26 +1,9 @@
 name: "Setup Go Paths"
 description: Overrides Go paths like GOCACHE and GOMODCACHE to use temporary directories.
-outputs:
-  gocache:
-    description: "Value of GOCACHE"
-    value: ${{ steps.paths.outputs.gocache }}
-  gomodcache:
-    description: "Value of GOMODCACHE"
-    value: ${{ steps.paths.outputs.gomodcache }}
-  gopath:
-    description: "Value of GOPATH"
-    value: ${{ steps.paths.outputs.gopath }}
-  gotmp:
-    description: "Value of GOTMPDIR"
-    value: ${{ steps.paths.outputs.gotmp }}
-  cached-dirs:
-    description: "Go directories that should be cached between CI runs"
-    value: ${{ steps.paths.outputs.cached-dirs }}
 runs:
   using: "composite"
   steps:
     - name: Override Go paths
-      id: paths
       uses: actions/github-script@60a0d83039c74a4aee543508d2ffcb1c3799cdea # v7
       with:
         script: |
@@ -39,14 +22,6 @@ runs:
           core.exportVariable('GOPATH', gopathDir);
           core.exportVariable('GOTMPDIR', gotmpDir);
 
-          core.setOutput('gocache', gocacheDir);
-          core.setOutput('gomodcache', gomodcacheDir);
-          core.setOutput('gopath', gopathDir);
-          core.setOutput('gotmp', gotmpDir);
-
-          const cachedDirs = `${gocacheDir}\n${gomodcacheDir}`;
-          core.setOutput('cached-dirs', cachedDirs);
-
     - name: Create directories
       shell: bash
       run: |