The file limit on a Tyros3 is actually 500 per folder! (see note on page 33 of the 'Tyros3 Owner's Manual')
This limit is the same as my T4, however I find that as you approach this number in a folder, access to the folder slows down considerably, so it is probably better to set your own notional limit a little lower than 500. On my T4, 400 files does not slow things down significantly.
Note that the 500 limit actually applies to the number of displayable objects in a folder, which includes all files of the type relevant to a selection screen (eg. Style files in the Style selection screen), plus any sub folders in a folder (whatever type of files they may contain).
Note that you may well get an error message if you try to transfer too many folders at once, even if each individual one contains less than the maximum allowed.
You can get around this by connecting your T3 to a computer via USB in so called 'USB Storage Mode' as explained on page 97 of the Owner's Manual. Although the section in the manual specifically refers to Wave files and Song files, you should be able to see/manage/transfer any type of file when connected like this!
When connected correctly, the T3 internal HD should show up in Windows Explorer or whatever the Windows 10 equivalent is. It can take a while (even a few minutes) to connect, but when (if!) it does, the drive should appear under 'Computer' in Explorer, like a removable USB drive does for example. Once you can see it you can then manage files on it just like any other drive, and although the individual folder limit will still apply on the T3, you can transfer as many folder and their contents as you like in one go without 'upsetting' the Tyros OS
This method is also useful for backing up the T3 internal HD.