In Europe people generally use “Europe” and the EU interchangeably.
I’m not sure many people would include Russia in Europe in normal speech, unless they were a geographer in which case Russia is partly “Europe” in some cases I think.
Even when the UK was part of the EU if someone in the UK said “Europe” they meant continental Europe and someone in continental Europe would be unlikely to mean the UK if they said Europe unless they were using “Europe” as a shorthand for the EU. When the UK was in the EU a United States American saying Europe would probably not not be including the UK in their mental model of Europe and, indeed [0], might not be very clear on what the UK actually is, because that’s confusing for the countries they agglomerate into “England” which might also include Ireland. A United States American saying “Europe” most likely means “Paris” and then maybe France, Italy, Spain or Greece but probably not Germany which is definitely the EU and everything that is wrong with the EU. But maybe Switzerland, because that very European.
As a European I’m not even sure where Serbia is, or if it’s even a real country [1]. I thought it was capital of Albania [2] . Or possibly a region of North Macedonia [3]
[0] only some of what I have said should be taken even part way seriously. Very little in fact
[1] Obviously being satirical here
[2,3] Also real countries, also European, but not necessarily “Europe” and definitely not EU. Yet.