Locking trunk bags are available, but I really don't think they're the best solution. There aren't many of them, which means you don't have much of a choice of features. By definition, these are attached permanently to your rear rack, and if someone steals the bicycle, the locking trunk rack is theirs.
You have many options; here are the common types of cargo systems for bicycles.
You have many options for carrying cargo on a bike. For the kinds of items you describe, by far the most convenient carrying system is a wire basket. You can get ones that install on your front handlebars or on your rear rack, depending on personal preference or what kind of bike you have (and if you have racks already). You can also get a milk crate or a box and attach it to your rear rack.
Since a basket is attached to the bike, you don't need to worry about unhooking it from the bike when you lock the bike up. A cargo net is advisable with a basket, so that items stay put. However, they do make the bike a little bit more unwieldy and can rattle a bit. Also, small items can fall out, and contents are exposed to the elements.
Security: None, unless you carry everything along. (Not what you're looking for.)
A basket on a commuter bike:
The next most convenient way to carry small amounts of cargo is with a simple backpack. The bike is unencumbered with racks or baskets or panniers, but your weight is up high (unbalancing you a bit) and your back can get sweaty. However, a backpack is useful for many things other than bike riding.
This is the ultimate in security, but has the disadvantage that you need to carry it around.
These are bags designed to hook to the side of a bike's rear rack. Panniers are more suitable for longer trips, and can be expensive and a little fiddly. You can't really leave them on the bike when locking it up. These would be overkill for your situation, unless you ride in the rain a lot and need to keep things dry.
Security is nonexistent. If somebody wants these, they're theirs.
A bike with front and rear panniers:
Trunk rack bags:
A trunk bag sounds like the sort of thing you were thinking of. It's a small bag, about the length and width of a bike's rear rack, and generallyas high as it is wide. I only recommend one of these if you already have a rack. Capacity is smaller than most backpacks. They're if you don't want a basket or a backpack. Some models are fiddly to attach or detach.
Locking versions of these are available but they're heavy and much less flexible than their counterparts for motorcycles. Part of the problem is that a bicycle is much lighter than a scooter or motorcycle. Also, a rack can be removed from a bike by anyone with a 5mm allen key.
Trunk rack bag on a folding bike's rear rack:
Cargo trailers are available for bikes, and some can even be used as shopping carts. These are better for large grocery runs, and it sounds like you don't need a trailer at this point in time. Enclosed trailers are well-suited for riding in the rain.
Security: Very little, similar to panniers. Although you could get a trailer that converts into a shopping cart and take it with you, like this one. But it'd be overkill for small errands.
A trailer attached to a bike:
In summary, different kinds of carriers are good for different kinds of errands, but I recommend either a backpack in your situation. A locking trunk bag is only as secure as the rack on your bike, but may be useful if all you want is a deterrent.