Is it better to have multiple files in one folder, or multiple folders with fewer files?
It doesn't matter.
The reason this copy job is failing is because Windows Explorer needs to enumerate all of the files first so that it can show you a progress bar before it starts the actual copy process. It's the total number of files that Windows Explorer is struggling with, not the total file size, so it will fail regardless of how many subfolders are used.
I recommend using Robocopy for this. It's a file-copy utility built into Windows that doesn't show a progress bar and so is able to skip that initial enumeration stage, making it much faster and more reliable. Unlike when you copy using Windows Explorer, Robocopy instantly starts moving files as soon as it's invoked, regardless of how many files there are.
Try running the following command in Command Prompt. Be sure to adjust the source and destination paths to match those on your PC:
robocopy /e c:\users\sappharite\pictures "d:\picture backup" /r:1 /w:1
/e includes subfolders and Empty subfolders
/r:1 attempts 1 retry on locked files (the default is 1 million attempts)
/w:1 waits 1 second before retrying on locked files (the default is 30 seconds)