Below job Deployment runs the strategy matrix while job name set-environment-matrix constructs the strategy matrix variable ENV-MATRIX.

My requirement is to choose a different runner group called Dot-Shared or runs-on: "Windows-latest" if the job name contains Approvers else it should runs-on: "${{ needs.set-global-runner.outputs.runner_name }}"

  set-environment-matrix:
    name: Set Environment Matrix for ${{ inputs.customWorkflow }}
    needs: set-global-runner  
    runs-on: "${{ needs.set-global-runner.outputs.runner_name }}"
    outputs:
      env-matrix: ${{ steps.set-matrix.outputs.ENV-MATRIX }}
    steps:
      - name: prereq
        id: set-matrix
        run: |
          ...
          ...

          $envList = New-Object System.Collections.ArrayList
          foreach($envName in $QueryResult.EnvironmentName){

            $skipApproval = $QueryResult | Where-Object { $_.EnvironmentName -eq $envName } | Select-Object -ExpandProperty skipApproval
            Write-Host "skipApproval value for $envName is $skipApproval"
            
          $srepo="$sreponame/environments/$envName"
          $envuri ="$apiUrl"+"$srepo"
          try {
          $respEnv = Invoke-WebRequest -Uri $envuri -Headers @{Authorization=("Basic {0}" -f $base64AuthInfo)} -ContentType "application/vnd.github+json" -UseBasicParsing
          echo "respEnv: $respEnv"
          $sEnvs=$respEnv.Content | convertfrom-json
             } catch {
              Write-host "$envName not found"
              exit 1
             }
             $envList.Add($envName)
          }
          $EnvNamesJSONVariable.Add("ENVNAME",$envList) 
          echo "ENV-MATRIX=$($EnvNamesJSONVariable | ConvertTo-JSON -Compress -Depth 100)" >> "$env:GITHUB_OUTPUT"

  Deployment:
    name: ${{ matrix.envName }}
    needs: [set-environment-matrix, set-global-runner]
    environment: 
      name: ${{ matrix.envName }}
      url: "${{ steps.prereq.outputs.appurl }}"
    #runs-on: "${{ needs.set-global-runner.outputs.runner_name }}"
    runs-on: 
      if: contains(matrix.envName, 'Approvers')
      value: Dot-Shared
      else: ${{ needs.set-global-runner.outputs.runner_name }}    
    strategy:
      matrix: ${{fromJSON(needs.set-environment-matrix.outputs.ENV-MATRIX)}}

    steps:

      - name: Track & Record Approvers List
        run: |
          ...
          ...

Can you please suggest?