I just bought the sims 4 cats and dogs and the only folders I have in it is "_installer" "contents" "support" and "installer.plist" I don't have a mods or tray folder and they are not in those folder...
What you are seeing in the Program Files folder it is installed files of the game. Don't touch this! Turn on the game and second new folder of the game will be created. You will find this folder in the Documents/Electronic Arts/ The Sims4. You will have all these folders there. Tray and mods also.