Small claims courts typically have fairly low limits, much lower than what the insurance might pay for damages to a house or furniture and art (as described in the write up).
You might get the cost of the move restored, but that doesn't cover the cost of repairs, replacements, and restoration.
Many jurisdictions have doubled their small claims max in the past decade. It’s worth looking into.
In this specific case it does seem that the insurance company paid for the damages to property, so recovering some or all of the moving costs would be exactly what is needed.