Can you upload a custom background on the NTP? Some users have reported slow-loading issues, so if you test, make sure you wait a few to see if it loads.
Tried toggling Trackers & ad blocking and Block fingerprinting on/off at Brave://settings/shields?
Clearing history/cache for all time on the Advanced time at brave://settings/clearBrowserData, exiting, and reopening Brave?
Also, was wondering if this Brave GitHub issue report is related (same?) as your issue.
I am on win10 and had no problems with upload button at https://wetransfer.com/ using both Release and Beta versions with Shields up. My trackers & ads blocking is set to aggressive and block fingerprinting to standard.
Please post an update. I think providing additional information will help troubleshoot the problem. Take care.