As you are mentioning increasing the dpi: First you increase the ppi value, second this is the most unnecessary parameter for stock photography. There is only one reason, why this parameter exists: to translate the pixel values into inches. So a picture with 2000points may be interpreted as a 100ppi image, meaning that it will be interpreted as a 20 inch length, or a 200ppi image, meaning that it will be interpreted as a 10 inch length. Nothing, and I repeat nothing has been changed in any quality related parameters. So for convinience, leave the ppi value at 200 or 300, whatever your prefered value is, and don't consider it anymore. It's completely irrelevant.
The resolution, however, is probably the most intersting parameter that you can touch up. But increasing the resolution does not create new information, but that information does need to come from the neighboring pixels and gets interpolated. There has been big progress in the course of the last years in this, increasing the resolution of assets intelligently, trying to keep the sharpness, without introducing new artefacts. But there are limits to this method, as you have experienced.
For some uses, those limits are not important, for some other applications the limits and the loss of quality is a major issue. As for this reason, do not increase the size too much, so that the asset, when checked at 100% still holds the necessary sharpness, without introducing artefacts. But this means that your source imge needs to be perfect, which is rarely the case with generative AI. You need to fix rendering errors first, then scale up and fix upscaling errors and those rendering errors that you did not see during your first checking. It's not al all an easy and fast task.
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