You can use following code to get existing value:
Connect-PnPOnline -Url "SiteUrl" -Interactive
$page = Get-PnPClientSidePage "Test.aspx"
$listItem = Get-PnPListItem -List "Site Pages" -Id $page.PageId
Write-Host $listItem["Department"]
You can use following code to set value:
Connect-PnPOnline -Url "SiteUrl" -Interactive
$page = Get-PnPClientSidePage "Test.aspx"
$listItem = Get-PnPListItem -List "Site Pages" -Id $page.PageId
$listItem["Department"] = "Department1"
$listItem.Update()
$listItem.Context.ExecuteQuery()
Make sure that in $listItem["Department"]
you use correct internal name of of your field. Check this to get your internal name of the field.