When overwriting the output file, this is what is happening in different QGIS versions and different use cases. In most cases, data is successfully processed despite messages. Although sometimes you have to refresh the map to see changes.
Case
3.16.5
3.22.2
Output file not loaded in canvas but exist
ERROR 1: C:\Users\asiddiqui\Desktop\plugin_test\Runoff Local.tif, band 1: Write operation not permitted on dataset opened in read-only mode 0.. Block writing failed
No Error Message
Output file loaded in canvas
ERROR 1: C:\Users\asiddiqui\Desktop\plugin_test\Runoff Local.tif, band 1: Write operation not permitted on dataset opened in read-only mode 0.. Block writing failed
[WinError 32] The process cannot access the file because it is being used by another process: 'C:\Users\asiddiqui\Desktop\plugin_test8\Runoff Local.tif' Process returned error code 0
When overwriting the output file, this is what is happening in different QGIS versions and different use cases. In most cases, data is successfully processed despite messages. Although sometimes you have to refresh the map to see changes.
A ticket has been filed with QGIS https://github.com/qgis/QGIS/issues/47233