Bumblebees famously cannot fly under fixed wing aerodynamics--and they don't. Rather, they "row" the air, moving their wings back and forth and varying the pitch to push air down like a reciprocating helicopter blade.
Clearly, this style of hovering flight works at larger-than-insect scale, because it's also how hummingbirds hover. But just how big can a creature using this flight mode get?
Warning, this answer involves a teeny tiny bit of fluid dynamics, a field that I'm largely unfamiliar with. Take it with perhaps a larger pinch of salt than usual.
Clearly, this style of hovering flight works at larger-than-insect scale, because it's also how hummingbirds hover
The style of hovering used by hummingbirds looks superficially similar to that used by bees, but there are quite a few differences. Even amongst insects, there isn't any one characteristic that defines insect flight, but a whole bunch of techniques, several of which may be employed by any one species depending on what it is doing.
Let's say, though, that what you want is something that can flap, hover, and fly backwards*, but you don't care too much about precisely how it does it. Hummingbirds are the only birds that can do that, and the largest hummingbird weighs about 20g and is about 21.5cm across. There's some small scope for scaling that up without hitting the maximum theoretical metabolic limits for such an animal, but not by much. This is slightly larger and much heavier than the largest living damselfly, and it has been noted that contemporary dragonflies are operating at their respiratory limits. Prehistoric Meganeura were much larger, up to 70cm wingspan, but probably had the benefit that they were living in an atmosphere with higher oxygen levels. Given their shape and diet, they were probably able to hover and fly backwards like their modern cousins.
That size is important. One of the magic numbers governing fluid dynamics is Reynolds number, which is (very loosely speaking) an indicator of how viscous a fluid is. For most real fluids, this figure is scale dependent. Air feels much more viscous for tiny insects like fruit flies, so they can use different flapping strategies to larger animals like swans, who don't have to contend with viscous forces so much. Flight strategies that work at one Reynolds number become increasingly less likely to work for flyers which operate in very different Reynolds numbers... what works for the fruitfly won't work for a Quetzalcoatalus. Whilst the oxygen content of the air in the carboniferous might have been higher, the Reynolds number for things the size of Meganeura would be pretty much the same now as it was then.
This suggests that this style of hovering flight could work for a medium-sized bird... probably smaller than a goose or carrion crow, but larger than a giant hummingbird. It would need to be at least as aerodynamic as a Meganeura, and probably have similar weight (allegedly about 450g, though I haven't found sound sources to back up that figure), wing size and wingbeat frequency. The main difficulty will be ramming enough oxygen and energy-rich nutrients into your flyer to prevent it from fainting or starving. Or being eaten by some other animal.
*note that if you dispense with the "flying backwards" requirement then it becomes a lot easier... larger birds of prey like the common buzzard can hover, and have wingspans of over a meter and bodyweights of over 800g, and their strategy probably scales up better than the fancier hummingbird-like style of hovering flight.
