Ahhh ... now I understand why you want to do this.
It turns out that like you, I also find it very useful to have a record of what applications I have used on an image, especially when I might have tried two different approaches on an image.
The problem with trying to use the editing metadata to keep track of this is exactly what you found: not all applications write to the editing metadata, and not all applications display it fully.
So, if you look back at almost every image I've ever posted on this forum, you'll see that my technique is to incorporate this info into the file name. For example:
d7b_1234nef-DxO-ps01a_16bpc_sRGB.psd
These are only for my own uses. I always rename the final image going to the client as something more meaningful to them while preserving the unique identifying info, e.g.:
Client_name-Model_or_product_name-shoot_date_and_time-d7b_1234-2000x1500px_sRGB.jpg
Some people don't like the resulting long file names, even if it's only for their own cataloging system, and instead will either indicate the processing steps by a color label (visible in many, but not all applications, and often the colors in one application aren't the same as in another) or, even more simply and reliably by adding the info to the caption or keywords of the image (a metadata field that is almost never unintentionally mucked with by editing software). Also, in case you are good at this, there is always the possibility of adding your own custom metadata field to some types of images, but then only you will likely ever see it or even know it's there.
HTH,
Tom M