Label time_data.dat and io_time_data.dat columns by what they measure

[sbryngelson]

Description

The time_data.dat header calls its second column s/step, but the value is the fastest single RK stage, i.e. one RHS evaluation. For RK3 that is about a third of a step, so anyone reading it as a per-step time underestimates cost by about 3x. The io_time_data.dat column is also labelled s/step, but it holds the mean time of one s_save_data call.

Root cause. Since #1650, s_tvd_rk sets time_avg to the minimum wall-clock time over individual RK stages, which is the right input for the grind time (ns/gp/eq/rhs). The header written in s_save_performance_metrics was never updated.

Fix. The headers become s/rhs and s/save, and each gets a one-line comment. Columns, values and formats are unchanged. The only parser in the tree (helpers.mako, which reads the last column of the last line) is unaffected. An existing time_data.dat keeps its old header, because rows are appended.

Verification

I ran a 1-rank run of a small 2D case on a Frontier CPU compute node (GNU 12.3):

time_data.dat:
     Ranks          s/rhs   ns/gp/eq/rhs
         1     0.00137424   143.82386185
io_time_data.dat:
     Ranks         s/save
         1     0.01753200

simulation compiles with CCE 19 (CPU) and GNU 12.3. Precheck passes, apart from two test_thermochem cases that fail on the Frontier login node because they compile with the system /usr/bin/gfortran (addressed by #1943). Results do not change.

Contribution Policy

We do not accept pull requests generated primarily by AI without genuine understanding or real-world usage context.

All contributions are expected to demonstrate:

• A clear understanding of the codebase
• Alignment with product direction
• Thoughtful reasoning behind changes
• Evidence of real-world usage or hands-on experience with the problem

If these expectations are not met, we would prefer to implement the changes ourselves rather than spend time reviewing low-effort submissions.

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Acknowledgement

• I confirm this PR meets the above expectations and reflects my own understanding and real-world context.

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This PR was prepared with the assistance of an AI tool (Claude Code). We hit this while reading timings from production runs on Frontier.

PR template credit: junegunn