I am the author of ChestSort (www.chestsort.de) and I have been asked to add support for Slimefun's backpacks.

To do this, I will have to check if an instance of Inventory belongs to a backpack. Is there some way to do this using your API?

There is not afaik. Definitely no exposed way to do that at least.
But please don't abuse the bug tracker for this, we have a discord server for questions / requests.

Not even sure whether the current system would even allow something like that in the first place.
But it's open-source so there is little that a PR can't fix or add ;)
Maybe someone on discord has some thoughts on how you or them can implement it.

Sorry, I didnt mean to mark it as bug, but there was no other way to open an issue.

Yeah, again we usually handle questions or requests over on discord: https://github.com/TheBusyBiscuit/Slimefun4#discord

Especially because I think that this may require a pull request to be made, I'd highly suggest you to ask someone there. I am sure someone over on discord may either help you with it or even pr it themselves.