How to cap ImageSize at the notebook width?

I'm not sure it is what you want, but have you tried

CurrentValue[EvaluationNotebook[], "GraphicsBoxOptionsImageSizeRaw"] = 500

This instantly resizes all graphics inside a notebook to 500 pixels as long as your notebook window is large enough.

As @Kuba pointed out, this can be used as option for Graphics

Graphics[{Circle[]}, 
  ImageSize -> Automatic, 
  BaseStyle -> "GraphicsBoxOptionsImageSizeRaw" -> 200]

Another possibility due to @CarlWoll is

Graphics[Circle[], ImageSizeRaw -> {500}]

How I found it

Initially, I was sure I had seen an option for that so I looked through

AbsoluteOptions[$Notebooks]

It turned out that what I had in mind was the option "DefaultNewGraphics" which is something else. My next thought was that it is very likely that this is exposed through CurrentValue. We have a question about all possible current values which led me, only the devil knows how, to this pastebin. A quick scan revealed the "GraphicsBoxOptionsImageSizeRaw" setting.

This is not a general solution but an improvement for Dynamic approach. It will run completely FrontEnd side:

Graphics[Circle[]
  , ImageSize -> Dynamic @ If[
        FEPrivate`Less[CurrentValue[{WindowSize, 1}] - 100, 500]
      , Full
      , 500
      , 500
    ]
]

-100 is unfortuantely manual, will try to get margins+toolbars width somehow.