@OscarLevin
I'm a little confused as what you're describing is not consistent with my experience. For my "on paper" assignments, I don't have the ability to download or upload submissions because Canvas doesn't have a submission file associated with it. For some types of online submissions, I can download or re-upload submissions, but I'm not sure how you're able to submit work on behalf of a student for an "on paper" assignment. When I reupload submissions, it doesn't replace the original upload, it adds a submission comment, so I'm not following you there, either. When I download the files, make changes, and reupload them, they don't see my changes in SpeedGrader. They see a comment that says "See attached file" and then they can download it.
It seems that the most straight-forward way to handle this would be for you to make it an online submission and then make the student take a photo of their paper and upload that into Canvas as well as turning the paper in to you. I don't have a cell phone (I have an old one that I use for multifactor authentication but it doesn't actually work as a phone), but I'm in the minority. Almost all of my students had smart phones where they could take a picture, convert it to a PDF [if that's what you wanted], and then upload it into Canvas. For the very few who couldn't do that, you could do that for them.
Then Canvas has an electronic copy and you have a paper copy to make sure that they actually did the work. You can download their submissions so that you have the properly named files. Then you either (1) grade the paper, scan, split, rename them using the existing names, and then reupload them, (2) grade the electronic submissions to save the scanning, splitting, and renaming, or (3) grade the electronic version using SpeedGrader.
When I did on paper assignments, I either provided feedback in Canvas as a submission comment along with a note that "this will make sense when you get your paper back" or "more information is provided when you get your paper back." I was basically leaving a comment about why they got the grade they got. I based subsequent due dates on having enough time to get the feedback back to them in class the next class period and then letting them have time to react to it.
I rarely took the time to scan the paper and go through all the extra steps you describe, it really was just too much work. But more power to you for wanting to get the feedback to them right away. You care more than most of them do -- especially those who are using AI to do their work.
There is an API call to do the bulk update of submissions. Uploading files into Canvas is not trivial. It's a three-step process (although step 3 is sometimes optional) and then you have to keep track of those file IDs for each student before you can do the bulk update of submissions. The built-in reupload of files provides a much smoother integration.