to_input_dataframe() drops dataset inputs for variables with formulas, such as state_pension_reported #2297

What happens

Simulation.to_input_dataframe() leaves out values a dataset supplies for a variable that has a formula. A simulation built from the exported frame then recalculates that variable instead of using the data, so it does not give the original's results. state_pension_reported is one such variable: the reloaded simulation pays no State Pension.

Reproduction

Run on #2270's branch with policyengine-core 3.32.27 and with 3.33.2; both print the same. The frame has one person, so it also loads on main:

import pandas as pd
from policyengine_uk import Simulation
from policyengine_uk.data import UKSingleYearDataset

data = UKSingleYearDataset(
    person=pd.DataFrame(
        {
            "person_id": [1],
            "person_benunit_id": [1],
            "person_household_id": [1],
            "age": [71],
            "state_pension_reported": [9_500.0],
        }
    ),
    benunit=pd.DataFrame({"benunit_id": [1]}),
    household=pd.DataFrame(
        {
            "household_id": [1],
            "household_weight": [1.0],
            "region": ["LONDON"],
            "council_tax": [0.0],
            "rent": [0.0],
            "tenure_type": ["OWNED_OUTRIGHT"],
        }
    ),
    fiscal_year=2025,
)
original = Simulation(dataset=data)
frame = original.to_input_dataframe()
print([c for c in frame.columns if "state_pension" in c])  # []
print(original.calculate("state_pension", 2025))                  # [9500.]
print(Simulation(dataset=frame).calculate("state_pension", 2025)) # [0.]

to_input_dataframe(include_computed_variables=True), taken before the simulation calculates anything, keeps the column, and the reloaded simulation then matches on every variable (tested in #2270).

Cause, read in the code

policyengine-core's to_input_dataframe exports a variable only if Variable.is_input_variable() is true: no formulas, and no adds or subtracts (_is_exportable_input_variable in policyengine_core/simulations/simulation.py). state_pension_reported has formula_2022, which returns the previous year's value, so the value the dataset supplied is not exported. Any dataset column for a variable with a formula or adds is dropped the same way, such as a supplied consumption.

Options

1. Give the UK Simulation its own to_input_dataframe that exports every value the simulation was given as an input and still stores, whatever the variable's formula. policyengine_uk.utils.supplied_inputs already tracks those (and Give UK simulations a working subsample #2265 adds supplied_input_arrays).
2. Change the rule in policyengine-core to export supplied inputs of formula variables.

Either needs a test that a dataset-built simulation's default export reloads to the same results when the dataset supplies a formula variable.

Found while fixing #2266 (#2270 documents the limit in its tests and does not change the export).