When you save a BP using Ctrl + S or by clicking the button you are executing a command that calls FAssetEditorToolkit::SaveAsset_Execute (binded in FAssetEditorToolkit::InitAssetEditor).
This function will get the Objects to save, as well as the associated packages.
It then calls FEditorFileUtils::PromptForCheckoutAndSave (This is where the prompt “what do you want to save” is managed if requested).
More info on the save prompt
The prompt is created using
FPromptForCheckoutAndSaveParams.
After a lot of code and some filtering the array of packages to check out will be sent to FEditorFileUtils::PromptToCheckoutPackagesInternal.
But it seems that there is another road, which ends in UPackage::Save2.
InternalPromptForCheckoutAndSave → InternalSavePackage → SaveAsset