One strong indicator of globalization is trade. The WTO maintains a set of global trade indicators, which has data on trade flows, trade disputes and tariff levels going back to 1948.
Some variables I would be interested in seeing tracked include:
I'm thinking a few things that are perhaps not super important individually, but ought to have at least some weight in such an index:
Standardization and transportation
what fraction of people are multiracial, and multiracial to which extent on average
Race being a construction, how would you measure this? Perhaps how widely the average person's genotype is distributed geographically?
Access to public utilities. I'm looking for global power, water, data, transport (both goods and people) and economic networks.
I have the impression that the more unified the world is, a) the less likely wars are, b) the easier it is to coordinate to solve global problems. It would also create more economic prosperity. But some forms of globalisation could also make our civilisation less robust. Anders Sandberg says the extent a feature is globalize should be proportional to the extent that feature's impact is global (https://www.youtube.com/watch?v=91FKgBURAV0).
I think a careful definition of just what unification will mean in this context. Based on a number of the metrics you list we could view just about every empire as a form/attempt of world unification. But that view strikes me as being very different from a world where people are freely moving and interacting with one another on a peaceful and largely voluntary basis.
I think the other important question here might be the end point -- what is such an index telling us or to be used for.
My view is that a fully unified world, on pretty much any definition I can think about, is unstable. So if the goal were to maximize the unification index that might be a very bad plan. If it was used to start tracking where we might start seeing increased tensions that might lead to increased global conflict/world war type outcomes perhaps it becomes a useful tool.
Of course, that is in the abstract as I'm not sure just how such an index would be assembled or over what time periods any given construction would be valid.
Relatedly: Does such an index exist?
Relatedly: What are relevant graphs / metrics / data on those variables?