Console rendering for problems reported via the Problems API

### Summary / Manifesto

In Gradle 9.3, we implemented basic command-line rendering for problem occurrences. This feature is currently limited, as problem occurrences are displayed only when the build is executed with the `--warning-mode=all` build option. We are seeking a more streamlined integration where the display of problems is the default mode of operation.

Stories:
- https://github.com/gradle/gradle/issues/36380
- https://github.com/gradle/gradle/issues/36382
- https://github.com/gradle/gradle/issues/36513
- https://github.com/gradle/gradle/issues/36514
- https://github.com/gradle/gradle/issues/36515

### References

- [Discovery document](https://docs.google.com/document/d/1z7kdsUO6OP8C6fYBY1vK38IPH2vFLOFb0jesvWc4DA0/edit?tab=t.0)

### Follow-up work

- https://github.com/gradle/gradle/issues/37339
- https://github.com/gradle/gradle/issues/37340
- https://github.com/gradle/gradle/issues/37341

Start with the linked Discovery document and the five story issues to understand the intended console-rendering scope and existing implementation. Trace how problem occurrences are currently shown only with --warning-mode=all; done should be defined by the stories and should cover default problem display, including the listed follow-up work.

Written by the indexing model from the issue text.