Quantitative Tempo and Rhythm Precision

I’d like to be able to track my progress in keeping tempo during my practice, not only in working towards increasing my speed, but also the precision of my timing as I work on being able to play faster.

(How) Do people assess the precision of their tempo of their practice performance over time?

I started using librosa beat tracking to plot tempo of rolling windows of my practice performance, as well as reference material. The plots help me quickly identify which phrases that I rush or lag. I can also track the standard error of my tempo day-to-day to see if I’m improving.

librosa’s onset detection helps me see if I’m ahead or behind the beat. Is there a quantitative way to summarize and track precision of practice performance so that I can see how/if my practice is improving?

Are there other/better tools or approaches to measure tempo and rhythm? I’ve seen that Yousician tells you if you’re late or early as you play along, but I didn’t see a summary of errors or performance. (And I want to practice with my own music.)

I realize that rhythm is only part of being able to play faster or more precisely, but I don’t yet know how to measure or summarize tone quality, dynamics, or other aspects…. There’s also the prospect of getting lost in the weeds dancing about architecture….
@Athenasius has a great summary of studies about perception of tempo changes providing some limits of necessary precision.