Rationale for this change

NameMappingProjectionVisitor.field (the visitor behind apply_name_mapping)
rebuilds each NestedField, but it passed the field's write default under the
keyword initial_write=:

return NestedField(
    field_id=field_partner.field_id,
    name=field.name,
    field_type=field_result,
    required=field.required,
    doc=field.doc,
    initial_default=field.initial_default,
    initial_write=field.write_default,   # <- no such parameter
)

NestedField.__init__ has no initial_write parameter; its write-default
keyword is write_default. Because NestedField is a Pydantic model, the
unknown initial_write key is absorbed by the **data catch-all and silently
ignored, so apply_name_mapping dropped every field's write_default to
None (while initial_default was preserved). Every other place that rebuilds
a NestedField (for example in pyiceberg/table/update/schema.py) already uses
write_default=; this was the one call site out of step with the constructor.

The fix passes write_default=field.write_default to match the constructor
contract.

Are these changes tested?

Yes. Added test_mapping_preserves_field_defaults in
tests/table/test_name_mapping.py, which builds a schema whose field carries
both initial_default and write_default, runs it through
apply_name_mapping, and asserts both values survive on the mapped field. It
fails before the change (write_default comes back None) and passes after.

• tests/table/test_name_mapping.py: 13 passed
• tests/io/test_pyarrow_visitor.py and tests/test_schema.py: 388 passed
  (the PyArrow name-mapping visitor and schema, the current caller surface)

Integration tests (Docker + Spark) were not run in this environment; the change
is pure Python type-plumbing fully exercised by the unit tests above.

Are there any user-facing changes?

No observable change in the current code paths. The only caller today is
pyarrow_to_schema -> apply_name_mapping (pyiceberg/io/pyarrow.py), which
feeds a PyArrow-derived schema whose fields never carry an Iceberg
write_default, so nothing is dropped in practice right now. This is a latent
correctness fix: it prevents write_default from being silently discarded the
moment a name mapping is applied to any schema whose fields set a write default.