Earlier quoted context omitted.
Possibly. I guess XUL was that API, but XUL is no more. It helps if your company uses the embedded stuff in other products. Like Microsoft used the Trident engine from IE6 all over Windows components. In that way, allocating resources for developing an embeddable engine is justifiable. Can Mozilla do that? I don'know. Google can (and does it! why wouldn't they?).
There is GeckoView on Android: https://mozilla.github.io/geckoview/ On desktop, it used to be available as an ActiveX component and a GTK widget, at least: https://www-archive.mozilla.org/projects/embedding/embedding... Wine still uses WineGecko as a replacement for IE engine – might also be worth looking into.
But sadly on Android the alternative is simply using a Chrome/Blink-powered webview, which is capable enough for most people and importantly comes at a zero APK size hit. So you need to have pretty special needs before including a complete custom browser engine inside your app becomes an attractive proposition.
(Whereas on Windows for example for a very long time the only OS-provided browser engine was IE, so if you needed more advanced web features, you couldn't avoid shipping your own browser engine in your application anyway.)