In SharePoint Online, add a new choice value to an existing choice field. The fieldname in the example is "MyChoiceField" with 3 very simple choices. A fourth choice is added by the script. A connection to the SharePoint site must be established.

AddChoiceToChoiceField.ps1

$field = Get-PnPField -Identity "MyChoiceField"

$ctx = Get-PnPContext

$fieldChoice = [Microsoft.SharePoint.Client.ClientContext].GetMethod("CastTo").MakeGenericMethod([Microsoft.SharePoint.Client.FieldChoice]).Invoke($ctx, $field)

$ctx.Load($fieldChoice)
Invoke-PnPQuery

$choices = $fieldChoice.Choices
$choices += "FOUR"

$fieldChoice.Choices = $choices

$fieldChoice.UpdateAndPushChanges($true)
Invoke-PnPQuery