The vacuum is full of spacetime, fields, virtual particles and other spicy wotsits. Lots of somethings but no nothings.
Just to be clear, according to the only type of theories that allow for virtual particles (QFTs), virtual particles are fields (that is, they are localized excitations of fields defined at every point in typically flat spacetime). Indeed, there is a related and important implication that follows from the fact that "particles" in particle physics are made to satisfy constraints imposed by QM and (special relativity) as well as certain more general considerations (e.g., microcausality, locality, the ability to consider systems as approximately isolated s.t. it can be safely asserted the system's processes and environment are sufficiently insensitive to any distant environment, system, etc., so that the effects of these on local processes are negligible). QM does not obey fundamental relativistic “laws” (non-relativistic quantum mechanics obeys Galilean symmetry “groups” and transformations that are only approximately correct when relativistic effects can be neglected). To construct a relativistic quantum theory that obeys the more fundamental “spacetime” symmetries (invariance under Poincaré group, loosely and incorrectly speaking), one has to deal with the fact that time is a parameter in QM while position in space is an observable. This is done by demoting the position operator and promoting observables themselves to the status of “particles” that are identified with the points they act on in spacetime and the fields that in a certain sense therefore cannot be considered apart from spacetime.
Moreover, you can’t have a vacuum full of spacetime or anything “full of spacetime.” Imagine a box. Inside that box there is a certain “region” of space at any particular time. It does not follow that the box contains “spacetime”. Objects in space carve out paths in spacetime, as even when they are (or can be considered to be) motionless in space they are (as is everything) moving in spacetime.
Quarks pop in and out of existence and are a type of particle that constitute matter.
Quarks are rather interesting, but not necessarily for the reason you give above (that's true of all "particles" in the standard model, not just quarks). Quarks are interesting because we have no real way in which to make sense out of them in QFT in the way one might hope in particle physics. They fail even the shaky, rather dubious mathematics of QFTs, e.g., in that the mathematical requirements we have for the "spaces" in which particles are defined don't work for quarks, they are tortuously difficult to work with even using an effective field theory approach thanks to the delicate balances needed to extracted physical values that can be compared to experiments, and they can't be observed. Ever.
I've seen this described in several ways in popular physics sources as well as textbooks and some other material: one may read or hear something like "quarks can't be observed in isolation" or "isolated quarks are never observed" or "quarks always come in groups, never singularly", but all this is at best a bad way to communicate that we can't observe them at all. Instead, such descriptions suggest that we can somehow "see" or detect quarks in HEP experiments like we do other "particles", but that when we do they are clustered together somehow, like common depictions of protons and neutrons as nice little balls "glued" together to make up the nucleus of an atom.
But to observe a physical system such as an electron or quark “in isolation” means “to observe it”, in the same way that even though all those proton and neutron balls can be individualized despite being seen all glued together into the nucleus in school models or pictures.
Quarks don’t have even the “quantum particle”-like realizability as the inability ot observe them in isolation actually means they are not even theoretically discernible, identifiable entities.
So in a more accurate but still misleading sort of way, you could say that things like electrons or pions or positrons “pop in and out of existence” more than do quarks.