Niels, I'm glad that you were able to resolve your issue and thank you for posting your solution so that others experiencing the same thing can easily reference this!
Since the Microsoft Q&A community has a policy that "The question author cannot accept their own answer. They can only accept answers by others ", I'll repost your solution in case you'd like to "Accept " the answer. Accepted answers show up at the top, resulting in improved discoverability for others.
Issue: Customer wants to create Blob Files and generate SAS URIs using a Logic App. When securing the Storage Account to allow access only from specific IP ranges, the Logic App connection fails, and the customer is encountering timeout errors.
Error Message: "The remote name could not be resolved: 'accountnamefromsettings.blob.core.windows.net'"
Cause: Whilst the designer gave the option to select the storage account from the dropdown, it didn't really select it.
Solution: Customer added the blob endpoint as a custom value and now the flow works with the IP restrictions active.