Key performance indicators or KPIs are "a measurable value that demonstrates how effectively a company is achieving key business objectives. Organizations use KPIs at multiple levels to evaluate their success at reaching targets." They intersect with the rise of SaaS applications at work quite well, but many organizations will struggle with defining how they intersect with soft skills they want their teams to acquire, even in a remote setting.
The tertiary KPI, for measuring performance improvement as a result of conflict resolution training and how they coincide with increases in productivity is difficult. However, increased customer engagement, overall employee satisfaction, and measuring employee retention, goes a long way toward measuring the efficacy of conflict resolution skills training in your organization. Of course, if you don't want to measure in these three areas, you could always track reductions in lawsuits and litigation efforts by employees, supervisors, managers, customers, and others.