I have made something similar, using IPTC (with https://github.com/james-see/iptcinfo3), but saving all parameters (even argv[0]) in the "caption/abstract", so you could copy and paste it into the command prompt to run it. Snippet:

parser.add_argument("--iptc", type=bool, nargs="?", default=True, help="save IPTC data to output image (only for JPG)")
# ...
fn = os.path.join(sample_path, "seed_" + str(opt.seed) + "_" + f"{base_count:05}.{opt.format}")
Image.fromarray(x_sample.astype(np.uint8)).save(
    fp = fn,
    quality = 95,
)
if opt.iptc and opt.format == "jpg":
    info = IPTCInfo(fn, force=True)
    cmd  = " ".join([f'"{x}"' if " " in x else x for x in sys.argv])
    info["caption/abstract"] = f"{cmd}{f' --seed {opt.seed}' if '--seed' not in cmd else ''}"[:2000]
    info["supplemental category"] = ["stable diffusion"]
    info.save(options="overwrite")

Result (as seen in Irfanview):

I wonder if using this format (reproducing exactly how the parameters are used in the input of the program) would be better, because it would make it easier to reproduce the original image (instead of doing a lot of copy-and-paste and editing)...

Some comments to this:

1. I think it is quite important to add this
2. This should also be added for the gradio stuff
3. PNGInfo will not work on jpeg files which are an option in the gradio scripts

Also, possibly using iTXT might be better since it supports UTF-8