Thanks to @Charlieface, I found a solution. I can just use the existing constructor and make Random Crn being readonly.

public readonly object Clone()
{
    Patient patient = new(_seed) {
        PatientCovariates = this.PatientCovariates.ToDictionary(
            entry => entry.Key,
            entry => entry.Value.ToDictionary(
                innerEntry => innerEntry.Key,
                innerEntry => innerEntry.Value
            )
    )
    };
    return patient;
}