There are browsers which are completely incompatible, like IE6. The message is for these.
Each browser implements different features. AppStudio has no idea which features your app uses, or whether a specific browser has a specific feature.
WebSQL is a good example. It’s present in Google and Safari (as well as mobile devices). The official position of the standards committee is that it is no longer being maintained and support may be dropped in future versions. (The reason is that it is based on a specific implementation, SQLite).
Opponents of the the WebSQL standard (and members of the committee) included Microsoft and Oracle, who have their own SQL products.
In an interesting twist, Microsoft announced yesterday that they will be replacing the guts of Edge with Google’s Chromium, which could result in WebSQL support being added to Edge.
The end result is that if you’re relying on a specific feature which may not be on all browsers, you need to test for it yourself.