What are some true customer centric metrics that your organization tracks? IE, the metrics your customers actually care about (not things like revenue or churn).

Net Promoter Score (NPS) will continue to be one of the most important customer centric metrics for CSM teams.  Customers also care very much about support levels, technical or customer support, tracking SLAs around the both of these are impactful.

The most common metric is probably Net Promoter Score.  Would your customer recommend you to another customer? I think you can also look at performance against SLAs, adoption metrics, product utilization, and Accounts Receivables (if they are not paying or consistently pay late, they are not happy)