You must be deluded to think Quinn is a side girl. Let me show you a couple of arguments that clearly condradict this:
* She has more sex scenes than any of the side girls (Lily, Riona, Jade, Camila, Cathy, Sarah, Melanie, etc.), often significantly more, and her amount of sex scenes is much closer to the main girls (who, aside from Jill, all have over 10). Quinn has exactly 10. Among side girls, Lily has 7, Camila 6, Riona and Sarah 5, Nicole 4, Jade 3, and so on. (I didn't count dreams or DnD for obvious reasons).
* She has more casual hangouts than the side girls. How many hangouts do you have with Camila, Lily or Jade besides fucking? Zero. Riona only recently got her first one and she is being built up by DPC as the most important side girl. With Quinn you have several of those.
* Since Ep. 4, DPC starts every episode (except 9) with a long flashback related to the main story. If we look at the subject of those flashbacks, it's like this: Josy & Maya (4), DIKs (5), Quinn (6), Jill (7), Bella (8), Maya's family (10). Judging from this, Quinn is treated on par with the most important characters of BaDIK.
* Quinn has much more lines of dialogue than any of the side girls and her amount of lines even surpasses some of the main girls, like Jill.
* In Ep. 8, when you have to choose your branch, you see pictures of all the girls you have some sort of a relationship with. For the side girls, you are able to see a maximum of 3 pictures and sometimes only 2. For the main girls, it's around 9. Quinn has 8, which again is a number much closer to the main girls than to the side girls.
* If you choose the Others branch in Ep. 8 while having successfully unlocked Quinn's path by helping her in Ep. 6, during the scene in Ep. 9 when you can message various girls from the Others branch, the option to message Quinn is the only one you are not allowed to skip.
* Finally, there is significantly more romance between her and the MC than with any side girl. She has her eyes on him since the beginning of Ep. 2 and practically in every episode there is something that pushes their relationship forward. I can give numerous examples if you want.
* She often appears among main girls in promo materials and in the background picture on DPC's patreon. People who say that she is there not as a LI, but as a representation of the Others branch, are wrong. If DPC wanted to show the branches on that picture, he would have to put Josy and Maya together as they are currently a single branch (even though they will probably split in the future).
What I listed above are the arguments which in my opinion prove without any doubt that Quinn is not a side girl.
But does this mean Quinn is one of the main girls? Even though there exists a basis to argue for that, I'd say she is something more close to a "hidden" main girl. She clearly has a different place in the storyline than than the official main girls. She is an antagonist in Season 1 (and even in Season 2, if you are following the Maya path) and is not presented initially as a dating option. It's just my guess, but I think DPC never made her a part of the official roster because he has a tragic end planned for her. There will be probably lot of shitshow and drama on every main path, but he probably planned a good ending for every major LI and possibly a shorter good ending for some of the minor LIs, provided the player makes the correct choices. But with Quinn I think he wants to give her a redemption arc (it was already started when she apologized to Tommy in Ep. 9 on every branch) that will have a tragic finale. Because DPC doesn't change the core story significantly based on a chosen branch (he only changes details), I don't think he would be willing to make this tragic finale dependent on the player's choice. And because he likes to be consequential when it comes to the game's design, he wants all the main LIs to have comparable endings, thus Quinn will never be treated officially as one of them.
As a fan of Quinn I'd love to be wrong about this and see a nice happy ending with her after Season 4. But right now, everything seems to point in the direction of her being destined for a tragic ending