This one clips on to my belt (which is covered by the shirt) that I wear all the time to hold up my trousers.
You could find something along the same lines to do the same job at a hiking store or similar. I like this one because I don’t need a separate belt also its pretty stiff canvas which as you can see doesn’t crush anything you put in there.
Then when you have it full all you need to do is take it off and tip the contents in to something larger and then set too and refill the pouch – hopefully many times over because I think most of us like our fresh soft fruits.
I’ve used this method for many years and find it handy not having to use one hand to hold a tray or whatever, it leaves both hands free for picking the fruit.