This is for 1.12.2. I know you're not supporting 1.12 anymore but it might be a quick and easy config option to add.

The backpack UI doesn't show when in the Baubles UI, for example, and many others.

I see the chest buttons have a forced GUIs config option, so if you could just add the same thing to the backpack GUI, that would be amazing! It would also allow better compatibility for https://www.curseforge.com/minecraft/mc-mods/backpack-baubles

If you are not able to do this, would you accept a pull request adding this feature? Thank you!

@ChloeDawn
Pulling Chloe into this, since she made the Quark Bauble Backpack mod from which this pertains to. Might be able to give insight.

This is not possible. Quark's backpack isn't merely a button that can be added to any GUI. It replaces the default player inventory entirely. To support other GUIs requires explicit support for each GUI layout.