ci: simplify how environment variables are used (#22067)

Having a clear separation between when we manipulate variables and when
we export them to GITHUB_ENV makes it less error-prone.

ci/before_cache.sh

@@ -7,10 +7,7 @@ CI_DIR="$(cd "$(dirname "${BASH_SOURCE[0]}")" && pwd)"
 # shellcheck source-path=SCRIPTDIR
 source "${CI_DIR}/common/suite.sh"
 
-mkdir -p "${HOME}/.cache"
-
-echo "before_cache.sh: cache size"
-du -chd 1 "${HOME}/.cache" | sort -rh | head -20
+mkdir -p "$CACHE_DIR"
 
 # Update the third-party dependency cache only if the build was successful.
 if ended_successfully && [ -d "${DEPS_BUILD_DIR}" ]; then