The first thing to do would be to go to the actions and look at the build log and specifically at the failed step (which most likely is going to be function deploying). Look at the error, good chance it is going to tell you what exactly went wrong.

If I had to make an educated guess, I'd say your service account doesn't have enough permissions (mine was setup with two - Cloud Functions Developer role and Service Account User) or the way you deploy the function isn't correct. I see that you are not exporting default credentials when you setup gcloud sdk, is there a reason for that?

Picture worth a thousand words - I've created a simple repo, where I have the most basic (default) python function that I deploy to GCF. Check it out, this should be enough to get you started.

UPDATE:
In case I decide to delete the repo one day, I am going to include the build yaml in here as well:

# This is a basic workflow to help you get started with Actions
name: CI

# Controls when the action will run. 
on:
  # Triggers the workflow on push or pull request events but only for the main branch
  push:
    branches: [ main ]
  pull_request:
    branches: [ main ]

  # Allows you to run this workflow manually from the Actions tab
  workflow_dispatch:

# A workflow run is made up of one or more jobs that can run sequentially or in parallel
jobs:
  # This workflow contains a single job called "build"
  build:
    # The type of runner that the job will run on
    runs-on: ubuntu-latest

    # Steps represent a sequence of tasks that will be executed as part of the job
    steps:
      # Checks-out your repository under $GITHUB_WORKSPACE, so your job can access it
      - uses: actions/checkout@v2

      - name: Set up gcloud Cloud SDK environment
        # You may pin to the exact commit or the version.
        # uses: google-github-actions/setup-gcloud@94337306dda8180d967a56932ceb4ddcf01edae7
        uses: google-github-actions/[email protected]
        with:
          
          # Service account email address to use for authentication. This is required
          # for legacy .p12 keys but can be omitted for .json keys. This is usually of
          # the format <name>@<project-id>.iam.gserviceaccount.com.
          service_account_email: ${{ secrets.SERVICE_ACCOUNT_EMAIL }} # optional
          
          # Service account key to use for authentication. This should be the JSON
          # formatted private key which can be exported from the Cloud Console. The
          # value can be raw or base64-encoded.
          service_account_key: ${{ secrets.SERVICE_ACCOUNT_KEY }} # optional
          
          # ID of the Google Cloud project. If provided, this will configure gcloud to
          # use this project ID by default for commands. Individual commands can still
          # override the project using the --project flag which takes precedence.
          project_id: ${{ secrets.PROJECT_ID }} # optional
          
          # Export the provided credentials as Google Default Application Credentials.
          # This will make the credentials available to later steps via the
          # GOOGLE_APPLICATION_CREDENTIALS environment variable. Future steps that
          # consume Default Application Credentials will automatically detect and use
          # these credentials.
          export_default_credentials: true # optional



      # Runs a single command using the runners shell
      - name: Deploy the function
        run: gcloud functions deploy myfunc --trigger-http --runtime=python39

As per the error seems to be you have given invalid json file of service account which is not parsed by the Git actions workflow. As per this official github :

1. (Optional) Create a Google Cloud Service Account. If you already have a Service Account, take note of the email address and skip this step :

    # TODO: replace ${PROJECT_ID} with your value below.             
    gcloud iam service-accounts create "my-service-account" \
      --project "${PROJECT_ID}"

2. Create a Service Account Key JSON for the Service Account.

# TODO: replace ${PROJECT_ID} with your value below.
gcloud iam service-accounts keys create "key.json" \
  --iam-account "my-service-account@${PROJECT_ID}.iam.gserviceaccount.com"

3. Upload the contents of this file as a GitHub Actions Secret. Use the name of the GitHub Actios secret as the credentials_json value in the GitHub Actions YAML:

 uses: 'google-github-actions/auth@v2'
  with:
      credentials_json: '${{ secrets.GOOGLE_CREDENTIALS }}' # Replace with the name of your GitHub Actions secret

Can you validate the above steps as per your yaml seems to be you need to give correct service account JSON file and also credentials json format need to be taken care.

---------- or else you can also achieve by using Workload Identity Federation through a Service Account by following this official github

Edit : Sinethemba Nontshintshi, achieved this by Changing the approach and used the Workload Identity Federation through a Service Account method to authenticate, by using this guide on how to set it up in GCP and in the YAML file it is passed as follows :

 - name: Authenticate Google Cloud             
   uses: google-github-actions/auth@v2             
   with: 
     service_account: 'your-service account'              
     workload_identity_provider: 'your-workload-identity-provider'