tl;dr; There are such indices, but no one is perfect. I go with SDR (XDR) for simplicity.
If you want inflation-adjusted, i.e. an index that will also take into account "global" inflation I found only one: World Currency Unit from Lingnan University, Hong Kong. Although they publish updated rates daily it looks a bit rusty and almost nobody seems to reference it. Besides there's no real API for it.
If you don't care about the inflation the simplest one to follow would be Special Drawing Rights from IMF. Many currency exchange sites include it rates and because of that it makes it easier to use than others.
There are other currency-basket indices that include more currencies including:
- WOCU from not-for-profit WDX Institute,
- FTSE WPU index, but unfortunately no ETF seems to follow it.
I personally pick XDR for simplicity.
Note that there's no one, global definition of "value". Say for example that you owe 1% of global wealth and because of productivity increase prices dropped for every service and products requiring human work. Are you more rich? You still owe 1% of total wealth, but you can buy more with it. Even if the answer is "yes, I'm more rich". How much richer are you?