JS code hardcodes the edit summaries for editing annotations (passed as parameters for #saveAnnotations) in English.
The hard part here is getting them to be in content language – ResourceLoader doesn't currently support that. We'd have to wait for T27349 or implement a subclass of ResourceLoaderFileModule that would handle it (example: MobileFrontend's MFResourceLoaderParsedMessageModule).
For now I propose leaving it as-is, we can push this once we need to (I think a beta cluster deploy can live in this state for now)
or implement a subclass of ResourceLoaderFileModule that would handle it (example: MobileFrontend's MFResourceLoaderParsedMessageModule).
For the interim I'd recommend going with a data module. This is an established, stable and supported pattern. (Either as plain class like VisualEditorDataModule, or as FileModule subclass if you only ever need it within one module; to reduce module noise).
ResourceLoader recently gained a $context->msg() method, for use as $context->msg() or $context->msg()->inContentLanguage() inside getScript. Together with enableModuleContentVersion() this should make for a simple and low-maintenance module.
The only catch is that you need to enumerate the keys inside the PHP class rather than conveniently listing them inside extension.json (though I suppose you could make it a constructor option actually, it's a fresh class after all). You'll need a JS identifier to stash them in, either specific to the extension or a good ol' mw.config key (don't use mw.messages).