So I ran into something that's kind of the opposite.
My Sim who lives in San Myshuno with his friends cooked a lovely meal and I couldn't drag it to the fridge, but I could tell him to put it away. (No Simple Living, worst fridge in the game.) Ditto my Sim who lives in Windenburg; I can't drag his food to the fridge but he can put it away. (No Simple Living, Schmapple fridge.)
I haven't tried with my Sims who do have Simple Living because I routinely drag it to the fridge myself. LOL
I... why can't I put my Sim's food into his fridge? Why does he have to do it?
I can absolutely open a bug report if you want, but it's kind of the opposite of the OP's issue. Let me do my own test tonight and I'll see what I can come up with. (I have mods--nothing crazy, MCCC, UI cheats, AllCheats, age check on roommate behaviors, cats can find things on other floors--but they'll want me to take them out.)
[Edited to add] - Okay, I just tested having a Sim put cooked food away with Simple Living, and she has the base game IceBOX Vintage fridge instead of the new one and is able to put food away fine, so I think it's the new fridge.
[Edited to add] Okay, so, I started a clean save with the mods folder dragged to the desktop and mods disabled. I was unable to reproduce this in Cordelia's Secret Cottage. I thought it might be the Budget Dee Lux fridge that lot comes with--the same fridge I'm having problems with in San Myshuno--so I bought the new vintage ice box fridge (that's the one you're having issues with, right?) and... nada. Will keep trying.
[Edited to add] Okay, guys, it's almost Critical Role time 😉 and I'm having no problems at all with the new ice box fridge and the Simple Living lot trait at Cordelia's Secret Cottage. I wonder if it's a weirdly placed light or something (I live in the Goth's Ophelia Villa in two different saves and Bella and Morty's En Suite eats Sims unless you delete the light (and sometimes the ottoman, the painting, etc., there's a bug report, other people say replacing the door helps). What lot are y'all playing on? My Sim only has $386 but I did attend the Romance Festival and loot the flowers, so we're about to be in the money. 😉
[Edited to add again] Okay, the save where I can't put things in the fridge? I can with mods disabled. Are you using mods?