So, take my site as an example. 
I want a little button just above the game so I can have the game expand into full screen mode
With stretching or with black borders? I use zoom in Embed mode and it looks blurry and bad.
I wish there was a way to zoom in but keep the graphics sharp
You mean upscaling? I mean, technically there are several different types of upscaling, but it depends on what you mean by looking sharp. You could upscale and keep the pixels, but make them bigger, but most upscaling uses some sort of blur or stretch, which gives it a weird fuzzy effect. It looks good on 3D games, but on pixelated games it doesn’t. If I hand draw my sprites instead of doing 16-bit, it would look perfectly fine, like for example my background of space is really high detail foe the current screen size, so it might look perfectly fine upscaled, but all my sprites wouldn’t. When I set the space background as my desktop background, it’s all low quality, stretched, and fuzzy, looks bad. Really all depends on the mode of upscaling I guess.
Upscale but not have blurry sprites