I have taken some unprintable images (too small or poor focus/sharpness) and enlarged to a massive size 6x-10x and then downsized the resulting gigantic image to something sensible using bicubic sharper (in Photoshop CC 2020) and the resulting image has been transformed and transformed for the better!
That's my experience, as well. I've licensed the Topaz product for a while now and I think it does a fine job within the constraints of what it is designed to do, but it can't work miracles—at least not yet: it has definitely been improving over time.
If I'm just trying to print from an otherwise well-focused image with inadequate inherent resolution for the desired size of the print (e.g., a crop of a high-resolution digital capture), I've found I'm almost always better off using Photoshop or simply relying on the Lightroom print module to manage the enlargement. A product like Topaz Gigapixel, which is analyzing an image and then building a replica of the image based on its machine-learning and internal logic, is more likely to introduce objectionable artifacts than a product that simply interpolates additional pixels into the destination image based on the pixels that are present in the source.
What Topaz Gigapixel excels at is taking low-resolution images such as scans of small retail-store analog snapshots and producing replicas that can be printed in a somewhat larger format. I've used it often to generate usable files from pictures culled from old family photo albums. Sometimes setting Gigapixel to make a large image and then reducing it in a photo editor helps to eliminate objectionable artifacts; sometimes Gigapixel works fine simply by setting it for the desired target size. I haven't come up with a technique for predicting which method works best, probably because there is no way for a user to know precisely what features the software is identifying in its analysis of the source image or how it produces similar features in the target.
Gigapixel also works well with non-photographic images, such as
those I have transformed by passing them through a convolutional neural network. Since these no longer contain the real-world detail provided by a photograph—they are simplified derivatives of their source images—Gigapixel seems to be able to accurately identify and reproduce the graphic elements that comprise them, and any artifacts it introduces are often not noticeable except on very close inspection. I suspect the Topaz software would work equally well with images made manually, either by analog methods (e.g., drawing or painting) or with digital design software.
