By now, it's well known that the FNaF3 minigames are memories from the FNaF4 bite victim. The parallel can be drawn simply by matching easter eggs to minigames, as I have done above. However, I think the connection goes a bit deeper than is usually acknowledged.
Notice the colors. The FNaF4 balloon kid has a pink balloon, and a solid red shirt. This does not quite match the real BB, but it does match the BB sprite from FNaF3. The kid's connection to the minigame is actually even stronger than the connection to BB himself.
BB's Air Adventure has clouds, meaning it's meant to be outdoors (It is an "air adventure", after all). This matches how the FNaF4 balloon kid is standing outside. On its own, this isn't a particularly meaningful connection, but as we continue, we will find that all of the minigames are actually consistent in this way.
Notice the windows. Mangle's quest is indoors, in a child's room. The platforms are purple, which loosely matches the pink aesthetic of the sister's room. It's also nighttime, which relates to the fact that this is a bedroom. The windows, though generic, look very similar to the window in Plushtrap's hall.
Again, none of these connections are very strong individually, but the fact that there's so many makes me think this was intentional.
The tiny toy chica is missing her beak, of course, because Toy Chica is specifically the player character of Chica's Party. The toy is sitting in grass, in a playground. Chica's Party has grassy green platforms, and it's filled with children, just like a playground would be.
Notice, again, the windows. Unlike in Mangle's Quest, these windows are lit up yellow. What this likely implies is that we are looking into a house, from the outside. This matches how the playground in FNaF4 is just outside the Afton house.
After this, the connections become fairly obvious. Stage01 is a very clear match to Fredbear's stage, which is also where RXQ's minigame begins, matching the shadows on the wall. Everyone knows that Happiest Day is the Bite of '83 backwards, though not everyone realizes that BV is parallel to the Puppet, not Golden Freddy.
I honestly find it confusing that it took so long for this connection to become popularly known. In retrospect, it seems obvious, especially with how blatantly FNAF World spelled it out.