I have a solution to this, using an orphan branch for the points status badge. I also had to fork and slightly modify the education/autograding action. (I’m sure someone else can come up with something better.)
I assume you are looking for something like this: 
Replace (or edit) the .github/workflow/classroom.yml
name: GitHub Classroom Workflow
on:
push:
branches:
- '*'
- '!badges'
jobs:
build:
name: Autograding
runs-on: ubuntu-latest
steps:
- uses: actions/checkout@v2
with:
fetch-depth: 0 # otherwise, you will failed to push refs to dest repo
# add id to action so outputs can be used
- uses: education/autograding@v1
id: autograder
continue-on-error: true
# make dir for badges
- name: badges branch and make dir
run: |
git checkout badges
mkdir -p .github/badges
# make points badge
- name: points badge
uses: emibcn/badge-action@v1
with:
LABEL: 'Points'
STATUS: ${{ steps.autograder.outputs.points }}
COLOR: cyan
path: '.github/badges/points.svg'
- name: Upload badge as artifact
uses: actions/upload-artifact@v2
with:
name: badge
path: '.github/badges/points.svg'
if-no-files-found: error
# commit and push badge if score has changed
- name: Commit badge
run: |
git config --local user.email "action@github.com"
git config --local user.name "GitHub Action"
git add '.github/badges/points.svg'
git commit -m "Add/Update badge"
continue-on-error: true
- name: Push badge commit
uses: ad-m/github-push-action@master
if: success()
with:
github_token: ${{ secrets.GITHUB_TOKEN }}
branch: badges
For the badge add the following to the README file

You can see this working here: https://github.com/markpatterson27/Simple-SQL-Exercise
[Edit: having read up a bit more on GH action outputs, I’ve realised points total is already exposed without having to fork the action. I’ve corrected the above .yml to reflect this.]