Hybrid/Branch Run Script Workflow Is Underdocumented

### **Background**

Recent user reports highlight that the E3SM run script fails in a non-obvious way for hybrid or branch runs when:

- `do_case_build=false`
- No existing executable is present
- The user expects hybrid/branch variables (`GET_REFCASE`, `RUN_REFDIR`, `RUN_REFCASE`, `RUN_REFDATE`) to be set in the case XML files

In this scenario, the script aborts at the `case_build` step, so `runtime_options` (where these variables are set via `xmlchange`) is never executed. This leads to default values persisting in the XML files, and users must manually edit them.

Additionally, confusion arises from the expected relationship between `CASE_ROOT` and build/run directories, which is not documented and can contribute to errors.

### **Requested Updates**

Note that pull requests have to be made for _two_ distinct repositories.

**1. Run Script Improvements**

These changes should go in [E3SM/run_e3sm.template.sh](https://github.com/E3SM-Project/E3SM/blob/master/run_e3sm.template.sh)

- Ensure that the script provides a clear, early error message when:
- `do_case_build=false` and no executable is present
- Hybrid/branch run options are set, but runtime_options will not be reached
- Consider refactoring the script logic so that `runtime_options` can be executed even if `case_build` is skipped, provided an executable exists (via `OLD_EXECUTABLE`)
- Add sanity checks or warnings for directory layout mismatches (e.g., when `CASE_ROOT`, build, and run directories are not colocated as expected)

**2. Documentation Enhancements**

These changes should go in [E3SM-Project.github.io/docs/running-e3sm-guide/guide-production.md](https://github.com/E3SM-Project/E3SM-Project.github.io/blob/main/docs/running-e3sm-guide/guide-production.md)

- Update the README or script header to clearly describe:
- Typical workflows for initial runs, hybrid/branch runs, and reusing executables
- Required and recommended settings for each workflow, including flag combinations (`do_fetch_code`, `do_create_newcase`, `do_case_setup`, `do_case_build`, `do_case_submit`)
- The importance of directory layout and how it affects script behavior
- That hybrid/branch variables are set during `runtime_options`, which only runs if the script reaches that stage
- Provide troubleshooting guidance for common pitfalls (e.g., why XML variables may not be set as expected)

### **References**

- Slack thread: [summary of user experience and debugging steps](https://e3sm-project.slack.com/archives/C04B3QGEQ/p1770329258241289)
- Possibly related PR: [E3SM #7580](https://github.com/E3SM-Project/E3SM/pull/7580) (recent hybrid case setup fix)

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**Summary:**
Update both the run script and its documentation to make hybrid/branch workflows less error-prone and more transparent for users. Ensure error handling and guidance are clear, especially around build flag combinations and directory layout.