I’ve been having this issue since the Jan 25th update. Anytime I load into a save, within a couple of seconds my sims freeze and will not do anything, qued up or not. The clock continues to move but ...
Ideas
Have you tried the "usual" troubleshooting tips including, and specifically, renaming your The Sims 4 USER FOLDER (the one located in Documents where the Mods folder is), launching the game so it creates a new USER FOLDER and checking if what you're experiencing is happening in a new save with a new household?
Also, try going OFFLINE in the EA App and in-game. Server connectivity can negatively impact gameplay (even though this is a single-player game). I've never had it impact gameplay as bad as you're describing but I have had my framerate tank from 60 FPS to 30 FPS.