You can use env at any level, since the root action, also in job and step.

I wrote a test action and a test script to validate it. Take a look.

The action file:

name: Env tests
on: push

env:
  FOO_ROOT: bar on root

jobs:
  test:
    runs-on: ubuntu-latest
    env:
      FOO_JOB: bar on job
    steps:
      - uses: actions/checkout@v1
      - name: Test envs
        run: ./env-test.sh
        env:
          FOO_STEP: bar on step

The script file:

#!/usr/bin/env bash

echo "FOO_ROOT: $FOO_ROOT"
echo "FOO_JOB: $FOO_JOB"
echo "FOO_STEP: $FOO_STEP"
echo " "
printenv

The results:

FOO_ROOT: bar on root
FOO_JOB: bar on job
FOO_STEP: bar on step

LEIN_HOME=/usr/local/lib/lein
M2_HOME=/usr/share/apache-maven-3.6.3
...

Check mine results here.

In fact, I don't know why it didn't work on you side, because, it must work.

You can use env at any level also in jobs and steps.

I wrote a test action and a test script to validate it:

The action file:

name: Env tests
on: push

env:
  FOO_ROOT: bar on root

jobs:
  test:
    runs-on: ubuntu-latest
    env:
      FOO_JOB: bar on job
    steps:
      - uses: actions/checkout@v1
      - name: Test envs
        run: ./env-test.sh
        env:
          FOO_STEP: bar on step

The script file:

#!/usr/bin/env bash

echo "FOO_ROOT: $FOO_ROOT"
echo "FOO_JOB: $FOO_JOB"
echo "FOO_STEP: $FOO_STEP"
echo " "
printenv

The results:

FOO_ROOT: bar on root
FOO_JOB: bar on job
FOO_STEP: bar on step

LEIN_HOME=/usr/local/lib/lein
M2_HOME=/usr/share/apache-maven-3.6.3
...

Check my results and, in fact, I don't know why it didn't work on your side because it must work.