Complete the FATES-CLM nitrogen coupling

[slevis-lmwg]

Description:

I started this PR with changes needed in ESCOMP/CTSM#3409.
So far that's just the renaming of
prt_carbon_allom_hyp to fates_c_only
prt_cnp_flex_allom_hyp to fates_cn

The corresponding ESCOMP issue:
ESCOMP/CTSM#3378

Resolves #1454
Reminder to address #1526

Collaborators:

@rgknox
@adrifoster

Expectation of Answer Changes:

I do not expect answers to change as a result of this PR alone; however, I expect answers to change for fates_parteh_mode = 2 as a result of the corresponding ESCOMP PR. So far I have not seen such diffs, while I have seen diffs for fates_parteh_mode = 1.

Checklist

All checklist items must be checked to enable merging this pull request:

Contributor

• The in-code documentation has been updated with descriptive comments
• The documentation has been assessed to determine if updates are necessary

Integrator

• FATES PASS/FAIL regression tests were run
• Evaluation of test results for answer changes was performed and results provided
• FATES-CLM6 Code Freeze: satellite phenology regression tests are b4b

If satellite phenology regressions are not b4b, please hold merge and notify the FATES development team.

Documentation

• Technical Note update:
• User's Guide update:

Test Results:

CTSM (or) E3SM (specify which) test hash-tag:

CTSM (or) E3SM (specify which) baseline hash-tag:

FATES baseline hash-tag:

Test Output:

[slevis-lmwg]

From meeting with @rgknox
We may decide to revert the parameter renaming, pending group feedback.
Keep the other changes!

[slevis-lmwg]

Ryan's update 2025/12/15:
"the team agreed at the fates software meeting that "fates_conly" and "fates_cn" were good names for the switch, both in the namelist and for the integer named constants that we pass between files"

In our meeting 2025/12/16 Ryan offered to change the integer values (1 and 2) to strings. (I made the change from hardwired values to named params in the code.)