Of course they have control over it, it’s literally their own platform. There’s no reason that Discord can’t benefit from the same optimizations that video games use. If a AAA title can figure out how to render 100000+ polygons UV wrapped with several 4K resolution textures in the span of 16 ms, then a $15B valued company can certainly figure out to display emojis and large images without turning your notebook into a DIY stovetop.
I assume Discord is built with electron. That should answer all your questions. Personally i dont use web apps on desktop..use discord in browser never had any issues