You can have criminal contempt in a civil case and criminal contempt in a civil case. The rules vary by state but in PA it’s civil contempt is used to force people to comply where criminal is punishment for disobedience.
What I mean is, the remedy for non-compliance with contracts, is fiscal, seizure, penalties of thus nature.
The goal of civil court is not the state punishing, but instead, laying out compensation, for damages, to the harmed.
There is no contempt of court for not paying these damages.
Then how does the civil court function? If nobody follows the courts order, the court is redundantly illegitimate.
No one is going to assault a cop, or have their bank shut down due to non compliance.
Where I am, what often happens is the damaged party has papers showing debt owed. It then becomes a colllection issue, sometimes, in some jurisdictions court takes an active role, in others, you have to do the work yourself.
Eg, you have to find their bank, hire a sheriff(the seizure kind), and go get what is now "your stuff".
Civil court works on fiscal, property to mitigate damage. If he is found to breach contract, a court could order seizure of assets (cash or property).
There could be punitive damages assessed too, if his actions are seen as purposefully malign.