No, you bought the bridge, Ethan, and now you have become one of them.
It is actually MC2 = E and not the other way around because the other way around would mean we know the total amount of E there is in the universe -- and we don't. We only know the E that got transformed into matter. We know nothing much about the E that did not transform into matter.
Spacetime is about the behavior of matter. It is not about space, it is not about time.
Would you say that the tape measure was involved with how tall you ended up being? Of course not. The tool is just the instrument that helps us place our own height in some measured perspective. The tape measure is not an active ingredient.
Same for spacetime. It is not an active ingredient in understanding the behavior of matter. It is a tool, a framework.
Take the clocks sent into space. Do you really believe the clocks showed that time dilated? Or do you recognize that the time displays showed how matter of the clock changed when placed in a spatially distinct location?
It should not surprise you that the data is the identical for envisioning Time Dilating and for envisioning Clock's Matter Changing.
We have to use our brains to understand the difference between A and B because only one is correct and no other means are available to figure out which is the correct one. The other is of course a brain fart, but not until we know with certainty that it is either A or either B, we have to use Occam's Razor. It makes time dilation the loser.
So, continue to say that the tape measure helped you growing to your current height, and we know that you bought the bridge.