RESOLUTION: After discovering a rather old BIS forums post directing me to the Win 11 OS's Ransomware Protection, I added all the newly reinstalled Arma .exe files to the allowed-through list and <boom>, the profiles dialog worked correctly and correctly accessed my existing operational profile and the editor accessed its mission files.
Something about the 00121 update triggered the OS to consider Arma a ransomware danger.

I've done fully checks of my win 11 system (chkdsk, mem chk, antivirus, defrag), reinstalled, revalidated. The .exe is set to run as administrator. After the 26 August 2026 update, my game lost my existing profiles and refuses to create a new profile that persists. It will temporarily create a "PLAYER 1" profile, but the next time I go into the profiles dialog, that one is gone. And I can't rename it after creating it or more profiles. If I save a mission as mpmission, it puts it into C:\Program Files (x86)\Steam\steamapps\common\Arma 3\MPMissions. I have tried keeping my old Arma 3 - Other Profiles folder and I've tried removing it entirely.

Title is insufficient -- hotfix 00121 is worse than just not finding the mpmissions folder. See description.