Can I interpret logistic regression coefficients and their p-values even if model performance is bad? I trained a logistic regression model with two binary variables $x_1$ and $x_2$ where my target binary variable is $y$:
$$\log\left(\frac{p}{1-p}\right) =\beta_0+\beta_1x_1+\beta_2x_2$$
Looking at p-values, we notice that $x_1$ has statistical significance (p-value < 0.05).
However, the model performance is terrible (pseudo-R-squared = 0.004552).
So I would like to know if it is reasonable to conclude that there is evidence that $x_1$ is related to outcome $y$ or not.

Note: I am using the statsmodel Python library

1893 observations is a lot. All kinds of hypothesis tests will yield statistical significance even for tiny effects if the sample size is large (we have many threads on this, here is a similar question on ANOVA I recently had).
Thus, it looks like there is signal in your data, it's just very weak. Some effects in the world are like this. Your model might indeed be the best you can do, or perhaps you can improve it (but beware of p-hacking!).
You can definitely interpret this, just keep the caveat about the weakness of the effect in mind.
