Let's take a look on what a background dependence may be.

"Background-independence is a loosely defined property of a theory of physics. Roughly speaking, it limits the number of mathematical structures used to describe space and time that are put in place "by hand". Instead, these structures are the result of dynamical equations, such as Einstein field equations, so that one can determine from first principles what form they should take. Since the form of the metric determines the result of calculations, a theory with background independence is more predictive than a theory without it, since the theory requires fewer inputs to make its predictions. This is analogous to desiring fewer free parameters in a fundamental theory. So background-independence can be seen as extending the mathematical objects that should be predicted from theory to include not just the parameters, but also geometrical structures."

But, can there be a dynamic structure that 'solves itself', without a cause? Yes, and no. We use constants for defining what is our common origin. Those are constant properties, principles, laws and rules, defining every point in a SpaceTime. Without them we get another 'physics' where nothing is true, everything a 'locally valid solution' but not joining it into a 'common SpaceTime', in short a 'magical universe'. You need something, that will join this SpaceTime. And then we have measurements.

My clearly defined measurement is what defines the reality around me, when we find us agreeing on them we finally get to repeatable experiments. But to me it's a 'sandbox of logic', 'inside' of which we find those constants rules etc etc. You can either choose to imagine dimensions as something existing in their own right. A 'commonly same global' sandbox', then also able to exist without interactions, aka connections, needed. Or you can do as I'm trying and define dimensions, aka SpaceTime, as a result of interactions (connections).

But there is a 'background' as I think, although of a very weird sort. I think I would like to call it 'information, constants, principles, rules, physical laws.. Joining a local definition of a SpaceTime into a common. Repeatable experiments.