In statistics, we formally define precision to be the inverse of variance.

The problem with comparing the standard errors of different regression coefficients in the same model is that the covariates may not be scaled. For a binary covariate, the standard deviation is at most 0.25, however continuous covariates can have arbitrarily large standard deviations. The regression coefficient is proportional to the standard deviation of the covariate. If they are not scaled, comparing their SEs is useless.

It is also incorrect to say that something is "precisely measured" because the inference on that regression coefficient is statistically significant. At best we can conclude that its value is non-zero, and cite a 0.05 (assumed) false positive error rate. Further, if the the null hypothesis actually is true, you may have a very narrow CI indicating a high degree of precision, yet this answer would suggest otherwise.

The way to answer this question is to appeal to what is known about the effect from previous studies. If these data come from a confirmatory type of study where there have been mixed findings, or similar reports on effects with 95% confidence intervals, you would use that knowledge to rank your study in terms of precision.

In statistics, we formally define precision to be the inverse of variance.

The problem with comparing the standard errors of different regression coefficients in the same model is that the covariates may not be scaled. For a binary covariate, the standard deviation is at most 0.25, however continuous covariates can have arbitrarily large standard deviations. The regression coefficient is proportional to the standard deviation of the covariate. If they are not scaled, comparing their SEs is useless.

It is also incorrect to say that something is "precisely measured" because the inference on that regression coefficient is statistically significant. At best we can conclude that its value is non-zero, and cite a 0.05 (assumed) false positive error rate. Further, if the the null hypothesis actually is true, you may have a very narrow CI indicating a high degree of precision, you wouldn't reject the null hypothesis because it's true, yet this answer would suggest otherwise.

The way to answer this question is to appeal to what is known about the effect from previous studies. If these data come from a confirmatory type of study where there have been mixed findings, or similar reports on effects with 95% confidence intervals, you would use that knowledge to rank your study in terms of precision.