So, you have two binary predictors, say $X$ and $Z$, and the logistic model $$\DeclareMathOperator{\P}{\mathbb{P}} \P(Y=1 \mid X=x) = \frac{e^{\beta_0 + \beta_1 x}}{1+e^{\beta_0 + \beta_1 x}} $$ setting $X=0$ you can see that $\beta_0$ is the log odds of probability that $Y=1$ given $X=0$. Now adding the sscond predictor in the model: $$ \P(Y=1 \mid X=x,Z=z) = \frac{e^{\beta_0 + \beta_1 x+\beta_2 z}}{1+e^{\beta_0 + \beta_1 x + \beta_2 z}} $$ and you can see that in this model $\beta_0$ is the log odds of the probability that $Y=1$ given both $X=0$ and $Z=0$ (in your code example you look at the conditioning $X=0, Z=1$).

So, you have two binary predictors, say $X$ and $Z$, and the logistic model $$\DeclareMathOperator{\P}{\mathbb{P}} \P(Y=1 \mid X=x) = \frac{e^{\beta_0 + \beta_1 x}}{1+e^{\beta_0 + \beta_1 x}} $$ setting $X=0$ you can see that $\beta_0$ is the log odds of probability that $Y=1$ given $X=0$. Now adding the second predictor in the model: $$ \P(Y=1 \mid X=x,Z=z) = \frac{e^{\beta_0 + \beta_1 x+\beta_2 z}}{1+e^{\beta_0 + \beta_1 x + \beta_2 z}} $$ and you can see that in this model $\beta_0$ is the log odds of the probability that $Y=1$ given both $X=0$ and $Z=0$ (in your code example you look at the conditioning $X=0, Z=1$).