Difference between ATE and mean of CATEs

Suppose that I want to estimate the price elasticity of different products within a category.
I start by estimating the average elasticity at the category level by passing X=None at the fit stage. I obtain a point estimate and a confidence interval.
Now I want to determine how the elasticity varies among products. I then specify a matrix X with dummy variables, each corresponding to a different product. I obtain point estimates and CIs for each product elasticity.
How can I explain that the mean of the product elasticities differ from the elasticity at the category level obtained in my first computation?
Moreover, the confidence interval for the mean product elasticity (obtained by calling PopulationSummaryResults) is also very different from the confidence interval for the category elasticity. When looking at the code, I see that this latter is built from the standard error of the mean point estimate ('stderr_mean') calculated as np.sqrt(np.mean(self.pred_stderr**2, axis=0)). Is it possible to have a quick explanation for this formula? Also, I would be interested in understanding why it is considered as a 'conservative upper bound'.
Many thanks in advance for your explanations.

Start with PopulationSummaryResults and the stderr_mean calculation shown in the issue, then compare the X=None category-level path with the product-level estimates. Document why the two estimands and their confidence intervals can differ, and explain the conservative-upper-bound interpretation of the formula. Done means the distinction and formula are clearly documented for users.