I've tested this a few different ways on Xbox Series X this afternoon and it's okay for me. I tested it by ordering on the phone and also by choosing the option to order groceries via the refrigerator. I tested on apartments too.
I wonder if the open Reaper event is interfering with it, if it's a new issue. What I would do is reinstall the game and packs. I'd also maybe check off the remaining Reaper challenge tasks before trying again incase that's affecting it somehow. Mine are completed until the next stage begins.
If that frozen screen happens again I'd power cycle the console. Save the game before trying to use the grocery option because if the screen does do that again and you have to powercycle the Xbox you'll be switching it off and will lose unsaved progress.
To powercycle, turn off your Xbox by pressing the Xbox button on the front of the console for about 10 seconds till it's shut down completely. Then unplug the power cable. Wait at least 10 seconds as this resets the power supply then plug it back in and turn the Xbox back on with the console button.
If the problem persists despite all of these suggestions, my next step would be to clear locally saved data. It can help when a game is misbehaving. So (with your game not running) go to Manage Game and Add-ons using the Menu button with 3 lines on it by clicking on Sims 4 on the console home screen. On the next page select Saved Data and you'll go to 2 sets of data. Pick the set of data next to your gamertag/username and be sure to only choose delete from console. Then immediately load up the game as usual and it will sync with the cloud as it's loading the game.
Hope something here helps.