I think it's inevitable that Google EU will be split off from Alphabet and Google US, into a stand-alone entity that the Europeans will regulate and mold as they see fit. It's the only possible positive end to the way Europeans largely view Google today (an abusive, dominant, foreign invader they can't compete with). After this many years, it's obvious the EU can't mount a competitive threat to Google's search monopoly, leaving only the alternatives of trying to cripple/restrict it through increasing targeted taxation & regulation (bad for the EU in the end, cutting their own nose off) or forcing a split-off that retains all the core capability & technology and can better adjust to what the Europeans want it to be (their culture, preferences, etc). The Google US and Google EU would then compete globally. Google EU would be operated from the various offices Google has planted around Europe. It would also immediately become Europe's largest technology company, surpassing SAP. I suspect that it would quickly begin having a ripple effect across the EU's tech landscape, in terms of investment and spurring more development.
Short of search becoming a lot less important soon... we had the baby bells, we'll have the baby Googles. The same goes for Facebook.
In some ways, Google is already more powerful than the EU. I am not totally sure that the EU could ultimately force Google to do anything it didn't want to do; many of the things that have been implemented putatively to limit the Goog have had the (un?)intended consequences of raising the costs and barrier to entry for new competitors and further cementing their dominance...
Google controls what 3 billion people see when they search for things -- what information they are exposed to. This is more control than any government of any sovereign nation in the history of humanity (more than the top 3 governments today combined) has ever had.
And please note that there are well-known processes by governments are held accountable by countries' constitutions and courts. A user of Google has no such recourse.
I don't think it's unreasonable that a company with impact larger than any single government in the history of humanity (yes, even larger than the EU) should have more than a little accountability. (Honestly, I think the Google board of directors should be elected at this point -- just like we elect leaders of governments -- but I know that's going to be a contentious view.)
Short of search becoming a lot less important soon... we had the baby bells, we'll have the baby Googles. The same goes for Facebook.