Yes, I do can the veggies. Lots of Green Beans and lots of pickles. Pickled Zuke spears, dill pickles, pickled beets and pickled green beans. Have done tomatoes, and made salsa.
Tomato harvest rarely gives me enough to do much with those. What we can’t eat, I stick in the freezer. Then use it to make soup or whatever in the winter.
The tomatoes don’t get mushy? What do you store them in?