To be blunt, I think they are critical. Data is the currency for any decision-making, and analytical competencies are exactly what empower product managers, technical or otherwise. For technical PMs, there is also an expectation of data self-sufficiency where they are not as dependent on BI or other engineers for extracting and analyzing data. While I wouldn't necessarily imply that SQL capabilities are absolutely critical, let's just say that analysis and visualization can be a substantial super-power. Whether it's being able to analyze feature-usage, page-flow dynamics, browser-metrics or build retention-matrices, using off-the-shelf dashboards can be limiting. Newly launched features may not always be accompanied by ready-to-reporting. In these cases, data competencies ca help a PM bridge that gap. Product managers who can access, analyze and visualize data also have a substantial speed and efficiency advantage over others.
What skills are useful? Specifically basic data-modeling, simple SQL, analytical tools for performing historgrams, scatter-plots and simple visualization using tableau, PowerBI etc. Another benefit to this data self-sufficiency is that PMs can engage in higher quality story-telling around their product area. It frees them to express what's happening using a data-centric or visual language that can often make the difference between a good PM and an exceptional one.