Well, it's not a pronoun, relative or otherwise.
Think of this as two sentences:
The third edition incorporated further improvements. The fourth edition incorporate further improvements as well
The as well could instead be in like manner, which denotes not only that it also had improvements, but that they were done in a similar way.
Or consider an equivalent formulation that has less extraneous details:
You have been to university, as have I.
Where you have a SVO sentence, it can be extended with such an additional clause specifying an additional subject for which the same sentence could be said.
Dogs have four legs.
Subject is dogs, verb is have, and subject is four legs.
Dogs have four legs, as have cows.
Cows, like dogs, have four legs.
The students in my day wanted to change the world.
Subject is students, qualified by "in my day", verb is wanted, object is to change the world.
The students in my day wanted to change the world, as do students today.
Students today also want to change the world.
The verb in the "as" clause is an auxiliary of some sort, and depends on the original verb and object of the main clause, and the tense of both the main clause and the as clause.
So, what this really means is that as has in your example might be thought of as relative (though not a pronoun), and its antecedent is incorporated further improvements.