Your run registry points to C:\Program Files (x86)\app\app.exe the reason is NSIS is 32bit application but that does not matter since windows can handle 32/64 run registry key.
If your old app is starting every time, and you have older files in the directory, it appears as SetOverwrite ifnewer does not work thus your files are not overwriten.
Personally I simply do not use SetOverwrite ifNewer, I simply overwrite files no matter what.
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