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: "Unable to create the type with the name 'AzureStorage'" in Visual Studio 2022 means that there is an issue with creating an instance of the 'AzureStorage' type.
Solution: Right-click on the SSIS project, go to Properties > Configuration Properties > General, and ensure the TargetServerVersion matches the SQL Server version you intend to use (e.g. SQL Server 2022) and Azure feature pack 2022 is installed. Also, a new Azure storage should be created and updated for each package. Make sure the AzureFeaturePack and TargetServerVersion should be same.
If your issue remains unresolved or have further questions, please let us know in the comments how we can assist. We are here to help you and strive to make your experience better and greatly value your feedback.
Please let us know if you have any further queries. I’m happy to assist you further.
Please do not forget to "Accept the answer” and “up-vote” wherever the information provided helps you, this can be beneficial to other community members.