Suppose I am having plugin version 4.0.3 in the source environment and version 4.0.5 in the target environment.
How can I upgrade the plug-in version from 4.0.3 to 4.0.5 without affecting the objects where it is used?
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Minor changes will not impact your app. Going from 4.0.3 to 4.0.5 is minor. For details, check the life cycle of plugins in documentation.
Update itself in cloud is: Just re-deploy. For on-premise it is: remove old, wait a bit, deploy new