How do I query GraphQL using SPE?

You can use the below function to query a defined GraphQL endpoint.

function Invoke-GraphRequest {
    param(
        [string]$query,
        [Sitecore.Data.Items.Item]$siteRoot,
        [string]$apiPath
    )
    
    $apiKeyItemPath = "/sitecore/system/Settings/Services/API Keys/key-name"
    $apiKeyItem = Get-Item -Path "master:$apiKeyItemPath"
    
    if (!$apiKeyItem) {
        Show-Alert "Unable to locate JSS API Key item at the following path: $apiKeyItemPath"
        exit
    }
    
    $linkOptions = New-Object -Type Sitecore.Links.UrlBuilders.ItemUrlBuilderOptions
    $linkOptions.AlwaysIncludeServerUrl = $true
    
    $homeUrl = [Sitecore.Links.LinkManager]::GetItemUrl($siteRoot, $linkOptions)
    
    if ([string]::IsNullOrEmpty($homeUrl)) {
        Show-Alert "Unable to get base url from home item: $($siteRoot.ID.ToString())"
        exit
    }
    
    $hostName = ([System.Uri]$homeUrl).Host
    $baseUrl = "https://$($hostName)$apiPath"
    
    $encodedQuery = [System.Web.HttpUtility]::UrlEncode($query) 
    
    $url = "$($baseUrl)?sc_apikey=$($apiKeyItem.ID.ToString())&query=$encodedQuery"
    
    $response = Invoke-WebRequest -Uri $url -UseBasicParsing
    
    $responseData = $response.Content | ConvertFrom-Json
    
    return $responseData
}

Usage:

$query = @"
        {
          search(rootItem: "{ADA8C66A-641F-45D8-B2E5-D3E757252CA2}", 
            index: "calendar_master_index",
            facetOn: [
              "service_location_facet"
            ], 
            fieldsEqual: [
              {name: "_template", value: "c746de598de3409f860071e5810c4d9e"}, 
            ]) {
            facets {
              values {
                value
              }
            }
          }
        }
"@ # this can't be tabbed over, or it will throw an error when imported

$homeItem = Get-Item -Path "master:/sitecore/content/site-name/home"

Import-Function -Name Invoke-GraphRequest
    
$responseData = Invoke-GraphRequest -Query $query -siteRoot $homeItem -apiPath "/api/graph-ql-endpoint"
    
$serviceLocationOptions = @{}
    
$facetValues = $responseData.data.search.facets.values
    
foreach ($facetValue in $facetValues) {
    $serviceLocationOptions[$facetValue.value] = $facetValue.value
}
    
return $serviceLocationOptions