The user.config file is created in the Local folder after checking the 'Write geoprocessing operations to XML log file' option in the ArcGIS Pro 2.9.x setting.
This behavior is not reproducible in ArcGIS Pro 3.0 nor the ArcGIS Pro 3.1 alpha builds on either English or Japanese Windows 10 21H1 64-bit. The user.config file is always written to %AppData%\Esri and not %LocalAppData%\Esri.
Upgrade to ArcGIS Pro 3.0. If the issue is not resolved after an upgrade, attempt the same workflow on the same machine, but logged in as a different Windows user. If the problem is not reproducible as a different user on the machine, contact your IT department to investigate and/or fix the Windows user profile.