Which tests are used to calculate the individual P-values in the Stata logit command (binary logistic regression)? This picture is from page 1290 in the Stata manual:

The model can be made with the following code in Stata:
use https://www.stata-press.com/data/r16/auto

keep make mpg weight foreign

logit foreign weight mpg

As I understand the overall fit for the model is calculated with a chi2 test (Prob > chi2 = 0.0000), but how are the individual P-values (P>|z|) calculated?

The tests shown by Stata for the individual coefficients are Wald tests whose test statistics have the form
$$
W_j = \frac{\hat{\beta}_j}{\widehat{\operatorname{SE}}(\hat{\beta}_j)}\sim N(0,1)
$$
Under the hypothesis than an individual coefficient is zero, these statistics will asymptotically follow the standard normal distribution. Hence, they are $z$-values. The corresponding $p$-values are calculated from the standard normal cdf $\Phi(x)$. Specifically, for two-sided $p$-values: $p=2\cdot\Phi(-|z|)$. For example in Stata for the coefficient for mpg:
di 2*normal(-abs(1.83))
.06724994

Reference
Hosmer DW, Lemeshow S, Sturdivant RX (2013): Applied Logistic Regression. 3rd ed. Wiley.
