I enabled the new 'Controlled Folder Access' option in Windows Defender, and it blocked SWTOR from creating screenshots and combat logs. (Settings files were okay.)

Once I learned this was the culprit, I just disabled the feature. But should you want to keep it enabled, use one of these exceptions to get SWTOR working again:

• The 'Star Wars - The Old Republic' directory (under Documents)
  
• The swtor.exe file (in swtor/retailclient under the main SWTOR program directory)
  

Note that after reviewing the Windows Defender event log, I learned that it blocks a lot of other programs as well. So correctly configuring the exceptions is important.

For anyone thats aware of that feature but doesnt know anything about it my understanding of that feature is it blocks pretty much all programs from accessing certain folders and for it to work, it needs to be configured to give access to those programs.

It can be a pain in the rear end to get it set up for all the programs that need access but once that's done it'll keep out all the nasty things like ransomware from affecting those folders (in theory, of course)