There doesn’t appear to be a widely used, systematic database dedicated to lens focus breathing. Unlike MTF, distortion, or vignetting, focus breathing is harder to standardize and quantify, so most sites don’t publish it as a regular test metric.

In practice, you usually have to rely on individual professional reviews and qualitative descriptions. Some reviewers do comment on breathing behavior, but coverage is inconsistent.

One indirect clue is lens design: databases sometimes note whether a lens uses internal focusing. Internal focusing can reduce apparent breathing, while unit-focusing or back-focusing designs are generally more likely to show it because the image circle changes with focus.

So the short answer is: there is no well-known comprehensive resource, and the best approach is to check detailed lens reviews and lens design notes rather than expecting a single centralized database.