Hi Gallatin 21V,
I understood that you are trying to update the tag on the APIM resource however this tag is append as a new one on the azure resource.
By default the Azure deployment is on incremental mode, Could you try deploy your using complete mode? use the what-if operation to verify that you only updated the resource that you want to update.
Example:
az deployment group what-if \
--mode Complete \
--name ExampleDeployment \
--resource-group ExampleResourceGroup \
--template-file main.bicep
References:
Let me know if this help you with what you are looking for.
Luis