Salam Saqib :)
When I tell someone that I went grocery shopping, I usually mean that I bought
food including fruits, vegetables, meat, yoghurt, chicken, cheese, crackers....etc
So the easiest way to say it in Arabic is: تسوّقتُ الطّعام/ تسوّقتُ واشتريتُ الطعام/ اشتريتُ الطعام