Hi @Piotr Kwiatkowski ,
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.
Issue:
The WildFly server where you deployed the application was causing an issue and overriding jackson dependencies configured in the app with predefined ones. This was triggering an error which stated that there were version conflicts, which initially seemed like they could be caused by an Azure dependency conflict with Jackson package versions.
Solution:
After replacing the predefined dependencies in the WildFly configuration, the problem disappeared and the Azure SDK created the blob container.
If I missed anything please let me know and I'd be happy to add it to my answer, or feel free to comment below with any additional information.
Please remember to "Accept the Answer" if any answer/reply helped, so that others in the community facing similar issues can easily find the solution.