Hi Travis,
It is for sure possible to use the GraphQL API to change product tags after a product is created, with the productUpdate mutation that can access the tags field.
After sending the mutation, check the response from the GraphQL API. If there’s an error in the mutation, the response will typically contain error messages that can provide insights into what went wrong.
When you update tags using the productUpdate mutation, the tags you provide will replace the existing tags. If you want to add or remove specific tags without affecting the existing ones, you’ll need to first fetch the current tags, modify the list as needed, and then send the updated list in the productUpdate mutation.
Hope this helps!