I'm working on a node which has a property which can be set in a input-element of type time. The user sets the value initially, but later on I want to change it from within the code.
How do I get the changed value back to the properties so that if the user inspects the node the updated value is shown?
You don't.
You can not update the stored properties of the node at runtime, you can change them based on inputs and use them as the flow runs, but the values set during a deploy are fixed and will be displayed if the user attempts to edit the node.
The only way to change these values is to redeploy the node (which can be done using a REST call to the Admin API, but this will interrupt the running of the flow as the node will be torn down and re-instantiated)