I don't know if there are canonical references for these measurements. I've found a couple references that seem good enough for an order-of-magnitude estimate, though.
Latour, A. W., Peterson, D. D., & Riner, D. D. (2019). Comparing Alternate Percent Body Fat Estimation Techniques for United States Navy Body Composition Assessment. International Journal of Kinesiology in Higher Education, 3(4), 93-105.
Latour et al compare gold standard estimates with Dual Energy X-ray Absorptiometry (DEXA) with US Navy-style estimates based on circumference. There are some differences according to how exactly circumference is used in the US Navy method, and differences for men versus women, but overall standard error of estimate ranged from 3.42-4.21%, in absolute percentage points, with Pearson correlations between methods ranging from .732 to .819. However, there was also an offset in their sample; the mean DEXA for men was 19.3 versus 16.1 using the Navy method, and DEXA for women was 26.9 versus 27.5 using the Navy method. This could reflect systematic differences in the population that the Navy estimates were based off of versus the study population in this study's sample.
He, M., Tan, K. C. B., Li, E. T. S., & Kung, A. W. C. (2001). Body fat determination by dual energy X-ray absorptiometry and its relation to body mass index and waist circumference in Hong Kong Chinese. International journal of obesity, 25(5), 748-752.
This study compared BMI and DEXA estimates and found a standard error of estimate of 4.6% in a regression with BMI only, and 4.3% including age; they also found a standard error of estimate of 4.4% using waist circumference (again, as far as I can tell these are all absolute measurements and assume normality of residuals). This is using an in-sample estimate of the correlation again, though, so you might expect errors to be greater in another population.
I think you'll find that these errors are large compared to the range of interesting variation in body fat. It seems that these estimates tell you very little compared to what would otherwise be apparent from visual inspection. BMI rather notoriously fails when applied to athletes and bodybuilders, for example, who can clearly be observed to have low body fat, whatever a BMI measurement would suggest.
In closing I wanted to again emphasize that these are absolute percentages, so if you estimate body fat % to be, say, 20%, and error is 4%, you would say that within 1 standard deviation you're looking at a range of 16-24%.