Tomato is vegetable plant , and can propagated by stem like almost vegetables plant such as potato sweet potato. That not reason to classify strawberry as fruit plant
Strawberry is a fruit plant as some other species from family Rosaceae, subfamily Rosoideae . First of all the fruits are sweet and people eat them like fruit. Second, strawberry plant can survive several years on same place and bear with fruits all time.
in fact some vegetable is sweet and eat like fruit such as watermelon, melon.
Classify of horticulture plant not need to plant family, some plant of leguminacea and solanaceae families (for example) is vegetable and other are forest.
Yes strawberry belong to Rosaceae family, but comparing with other plants in same family the horticulture practice is different.
Yes can strawberry stay in land for long time but the best practice is re-cultivated every year.
And some plant of vegetable can stay long time such as papper, sweet potato.
for strawberry understand with me , it is a fruit. for vegetable plant , the food for people eat is more interesting in cooked food, but this opinion is not absolution . for example ,there are some vegetable plants do not need cook, but more the fruit plant not need cook.