Hi @Maxim Rzhevskiy, 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:
Access denied to storage account from function app.
Solution:
The issue occurred because the Blob in Storage Account was set to Archive tier.
As mentioned in MSDOC, a blob in the archive tier is offline which cannot be read or modified until it is rehydrated.
While a blob is in the archive tier, it can't be read or modified.
To read or download a blob in the archive tier, you must first rehydrate it to an online tier, either hot or cool.
The rehydration process can take several hours and has associated costs.
Please remember to "Accept Answer" if the sol has helped, so that others in the community facing similar issues can easily find the solution.