Ideas
I have experienced something similar. On PC, only once did it result in a full crash, the other times Sims 4 becomes non-responsive when pressing C to take a screenshot.
I have observed the issue using the C for screenshots in both Cas and Build/Buy Mode. The only way to recover from the freeze or hangup is to force the game to close. It can be reproduced, but it is intermittent with no clear pattern outside of the fact that it is triggered with the C key. This issue happens with and without mods, with a cleaned/fresh Sims 4 folder, a clean install, and a repair. It will happen regardless of whether you are in Fullscreen, Windowed, or Windows Fullscreen mode. GPU and Windows are both fully updated. I don't use any overlays. I do have all of the packs installed. The Screenshot Pop-Up Is turned off. It also happens on new saves.
I can confirm that the issue seems to go away when switching from Direct X 11 to Direct X 9.