Where fine tuning shines imo:
Things that require consistency: e.g. you want the chat / output to have certain "personality", consistent level of conciseness or formatting.
Things where examples are hard to fit into prompt: e.g. summarization, or other longer form tasks.
High volume, simpler tasks: Various data extraction tasks.
Two of my side projects (links in bio) use AI for summarization, and indeed consistency is a big issue there.