What will happen if a brand new pvc pipe causes a sinkhole underground?

It means you did not glue the joint together properly and you will have to dig out the pipe and re do.  That is worse than putting the pipe in, so this is a mistake that you will do only once. Learn how to glue the pipe properly and hold the joint together until the glue sets. The joint kicks back when the glues sets and you have to hold it with some strength.  Don't use a repair fitting with an elastomer seal.  They are temporary and will leak someday.  Put in hard pipe with good joints.

Unlikely to cause a sinkhole, but it may cause subsidence. That's what you have insurance for.

pvc pipe on its own can't cause a sinkhole.   Unless its dumping its water underground to an theres a cavity for the saturated dirt to collapse into.
If you think you have this its probably the dirt settling from the loose dirt that the pipe was covered with.  You'll need to bring somemore dirt in to level it off.

The sink hole is a cavity somewhere under ground collapsing and its doubtful a pipe would do such a thing , unless it was leaking water profusely over a long period of time , sink holes are undeground mines and workings finally collapsing after years of neglect by humans