I think the term "Super Resolution" is misleading. Like Gigapixel AI, the Adobe Super Resolution algorithm attempts to add or refine detail as it changes the pixel dimensions of the image - it is fabricating data based on the AI training model, etc.
"Actual" Super Resolution refines the resolution and signal to noise ratio of an acquired image by combining multiple shots of the same scene, with slight variations in the viewpoint of the light ray hitting the sensor. Some cameras do this by using the IBIS mech on the sensor, shifting the sensor slightly for each image in the Super Res set it acquires. You can also handhold or slightly shift the camera on the tripod (just by slightly pressing against the camera or tripod) and get similar data. The images are then registered and combined to yield more detail and less noise at a higher pixel dimension. You can also downsize the Super Res image to the original pixel dimensions of a single image and get a much cleaner image file with more useable dynamic range.
Years ago, there was an application called "Photo Acute" that was, frankly, ahead of its time and performed several computational photographic tasks, including Super Resolution. Here is the website - still functional:
http://www.photoacute.com
but you can tell from the site verbiage and OS requirements it has not been updated for quite some time. Astrophotography also has several workflow options that perform some of the computational aspects of combining several images into a single working image file, but no so much for spatial resolution, more for increase in signal to noise ratio, given the very faint light that their imaging devices are trying to acquire.
The combination of many images into a single, higher pixel count image, can be done manually in PS and similar image editing software. Here is a proof of concept video using an image set acquired in burst mode on an iPhone:
https://youtu.be/vr7JoBGqoCk
When using multiple images shot with slightly varying points of view, one is actually gaining resolution (and SNR) compared to a single image. With the Adobe or Gigapixel AI approach, pixels are being fabricated. How well each workflow and result works for you is for you to decide! Give each technique a try with the same image data and see how much each result gives you what you want.
Kirk