Small plates Chinese actually does exist…the problem might lie in the execution and concept / delivery of North American restaurants to accommodate the format where restaurants decide to enlarge the portions and charge a higher price.
The easiest style I can think of is referred to as Shanghai Xiao Chir (small eats/small plates) 上海小吃. We used to have a hole in the wall Shanghainese in Northern California that has shuttered, but people in the know would go there because of the smaller portioned small dishes and other typical classics. They would include xiaolongbao (not necessarily in a form that’s great), maybe shenjianbao, but other dishes also such as marinated dried fried tofu in rice vermicelli (fen si) sometimes in a soup, soy sauce marinated stir fried bamboo shoots (usually quite greasy from the oil, but very aromatic), a smaller portioned size of scallions brothless noodles drizzled with oil made from stir frying scallions, pan fried noodles (similar to Cantonese style crispy noodles but pan fried till crispy on both top and bottom), Shanghainese eight treasures rice. Shanghainese style wonton soup etc etc.
The alternative to that might be the Taiwanese porridge restaurants where you get several plated entrees from the steam table. If the portion sizes are adequate enough for 3 to 4 people to order a larger number, then those would be the distant parallel to the Shangahinese style small plates. Not uncommon to find the aromatic greasy stir fried bamboo shoots, or a few of the other afforementioned Shanghainese style small plates at some Taiwanese porridge shops (at least this is the case for Northern California…can’t speak exactly to SoCal but hopefully not that far off).
It can’t be just Shanghainese style that does this approach, but this was quite common at least in Hong Kong several decades ago. I think at certain dai pai dong style restaurants in Hong Kong, there are wok stir fry portions that are adequate for multiple dishes for a table, yet they are referred to as wok hay stir fry small plates/small eats as a category. Not tapas size, but not seafood restaurant humongous entree either.
The closest thing and maybe the most accessible you can get, is if you go to a beef noodle or dumpling restaurant and order the cold dishes/appetizer plates that are not entree sized. Easy cop out, but I guess that’s better than nothing.