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

I just wanted to comment if anyone else is trying to do this - You could grab existing values and add it to a long string, then comma separate everything

[system.string[]]$Users = "Bradley Wyatt","Jason Portillo"
Set-PnPField -List "Onboarding" -Identity "Copy_x0020_User" -Values @{Choices=$Users}