Single-source OrtErrorCode values to keep StatusCode in sync (#29065)
### Description
<!-- Describe your changes. -->
Extract the public C API OrtErrorCode enum into its own header
(onnxruntime_error_code.h) and define onnxruntime::common::StatusCode
enumerators in terms of the ORT_* constants (e.g. OK = ORT_OK). This
makes the public C API enum the single source of truth for error code
values so the public and internal enums cannot drift out of sync,
without requiring any call-site changes to the existing static_cast
bridges.
Add the new header to the C/C++ API install list
(cmake/onnxruntime.cmake) and to the Doxygen INPUT list
(docs/c_cxx/Doxyfile).
### Motivation and Context
<!-- - Why is this change required? What problem does it solve?
- If it fixes an open issue, please link to the issue here. -->
`OrtErrorCode` may be added to in the future. This change makes it
easier to keep the internal enum in sync.
Follow up to
https://github.com/microsoft/onnxruntime/pull/29018#discussion_r3405250002
Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>