[64-Bit] Can't click anything to play beyond mod screen

@desia2003  Do you have any apps running that include overlays, for example Discord?  If so, please close them completely (Quit, don't just close the window) before launching Sims 3.  Disable the Origin in-game overlay too: hover over your username, select Application Settings, then Origin in-game, and disable the option at the top.

@desia2003  Are you playing in fullscreen or windowed mode, and does it help to switch?  Please try at the Main Menu with cmd-return: I'd like to know whether this works.  But if not, you can edit options.ini, in Documents > Electronic Arts > The Sims 3.  Search for "fullscreen" without quotes and set it to 1 or 0, whichever you haven't been using.

If this doesn't help, do you have use any accessibility settings or apps?  I've seen a couple of cases where this was the culprit.  You can try disabling the app or setting(s), or if you'd prefer not to mess with your current setup, you can instead create a new admin account on your Mac and change the settings there.  (Or just make sure you're using all default settings.)

@desia2003  You were actually in fullscreen mode the first time and switched to windowed by setting fullscreen to zero.  What I'm guessing is that the game window had black bars on either side, which is a compensation so the window doesn't stretch unnecessarily.

I don't know what settings or apps you might be using, and to be honest I'm not sure where to look since I've never used any of these features myself.  If you know what you've installed, or someone else in your household does, you can simply disable the relevant app(s) and go from there.  If you're not sure, just try playing in a new user account, one with all default settings, and see how it goes.  This doesn't entirely prevent apps from having an effect, but at the very least it should rule out any user settings specific to your current account.

@desia2003  That's quite odd.  Is the new account an admin account, and where was the original Sims 3 installed?  (I mean in the old user account.)  Regardless, you can get rid of the new account if you want; I suspect the two installs of Sims 3 are the problem here, or rather, Origin is still trying and failing to use the original install despite your having reinstalled.

In your main account, I'd be curious to know what user settings, if any, you've changed with regards to accessibility or the scaling of your monitor.

If you didn't see a change when editing options.ini, it's possible you were editing the wrong copy, as in, one that's in iCloud rather than stored locally on your computer.  The way to get to the latter is to open a Finder window and click Macintosh HD in the left panel, then Users > your username > Documents > etc.  If you don't see Macintosh HD, click Finder in the upper left corner, then Preferences > Sidebar, and check the box next to hard disks.