According to updated Eurovision rules, artists aren’t allowed to wave any pride flags on stage. While most pride flags have already been banned last year (Nemo, for example, wasn’t actually allowed to wave the non-binary flag), this now even includes the six-stripe rainbow flag.
However, before last year, it wasn’t something very special to also wave a pride flag or have one in the Greenroom.
That’s a good question. In the ESC context it’s more for identification, as the artist is participating for (the public broadcaster of) a country, the voting is executed and announced by country and not by the name of the artist.