[2020] In Game Screenshots F12 Does Not Work

Are you bypassing the launcher with the cities.bat file? That's known to cause issues with the overlay.

Btw F12 is also the game's own screenshot key, but those screenshots end up in a different folder, namely this one:
C:\Users\YOURUSER\AppData\Local\Colossal Order\Cities_Skylines\Screenshots

Try shutting down Steam completely, then right click on it and run as administrator. Might also be worth changing the shortcut for it to something different and then back to F12 to see if that solves it.

If none of that works, I'd try a reinstall of Steam.