By 2100, the European Union (NOT including Russia) will become a federal republic with a model similar to the United States, however, with many key differences. Individual European states will have some degree of legislative autonomy, however, they will also have their own official language(s) and native ethnicities, with the federal government’s capital being located in Brussels.
This may be controversial to some in the early-21st century, however, I believe the so-called “migrant crisis” of the 2010s has created an ever-growing and extremely-strong reactionary Ethno-European current that will effectively see the deportation of large swaths of migrant-populations as well as much heavier immigration restrictions in order to keep the continent ethnically and culturally European (already seen in countries like Denmark and Sweden, as well as a so-called “far-right” political party winning in Germany).
HOWEVER, this is NOT the same as the modern-day early-21st century EU, which is more of an economic and trade union with a shared currency rather than a full-blown federal republic. I actually believe that on a bureaucratic-level, individual European states will be very homogenous with one another, with the key differences between states being ethnicity, language, cuisine, etc…, although citizens within the federalized European Union will of course be able to move, work, and live freely within its borders, just as it is today. However, one key distinction is the federalized European Union has its own national military rather than individual countries having their own defense forces.
Culturally and economically, I foresee the United States and the European Union undoubtedly maintaining an extremely close bond which will recover from the mistakes made by the Trump administration as soon as Gavin Newsom is elected president in 2028. This model of a federalized European State that maintains individual European ethnicities and cultures makes the average European feel “safe” and the cultural, economic, and trade alliance with the United States is completely rational.