When you choose to export from Photo (File>Export), choose TIFF, 16-bit and you should get a full quality, uncompressed, but edited image out of Photo. This is what the settings in the export dialog box will look like:
The reason you haven't found the folder with the edits are that image editing programs such as Photo or Adobe Lightroom perform non-destructive edits as an instruction set that sits in a database that references the original image. Basically your edits just create a recipe that the software then can use to create an output file. If you choose to print, it will give the instructions on how to render the edited image to the printer. The only time you will get an edited file is if you export to a file format such as JPEG or TIFF.
TIFF gives you an uncompressed file, and by choosing 16 bits, the software is actually interpolating to add pixels to your photos as most digital camera sensors produce a 12 or 14 bit image. There isn't much of a point for more, as the human eye has a hard time distinguishing the available gradations of a 16-bit dynamic range.
JPEG is a Lossy compression format, but for even a 5K iMac, if you go for the highest quality, largest file size, you will likely not be able to see a difference between the TIFF and the JPEG version of the file, and you will have a file that is probably 80% smaller, depending on the subject matter.
You also have the option of exporting the Unedited originals (Raw files) using this option as well. There is an option to export IPTC data as an XMP sidecar file.
The short answer is you want your Mac to get out of CPU use so that iCloud photos will resume. Thermally cooling the case and/or quitting all other processes that use CPU would be warranted.
Since you're technical minded - you can dump the thermal stats to see if you feel you have a hardware issue or can shape the workload to relieve a proper thermal pressure warning:
pmset -g thermlog
The long answer is there are many throttles and other things that could go wrong with iCloud upload. Look at this reverse engineering of things in the plain files portion of iCloud file upload - let alone the more detailed Photos use that does face, moment, web app and more features in play like daily upload caps, uploads to shared storage being different than your iCloud storage and optimizing the versions when you run low on storage space.
Diagram from the amazing article by Howard Oakley - https://eclecticlight.co/2018/03/30/inside-icloud-drive-uploading-a-file/
Best Answer
You can run the following command from terminal to get your user account pictures. This would be an easy way.
Just you will get a 256x256 pixel version of your account picture