Millions of Ukrainians weren't feeling safe since at least 2014. But it doesn't give grounds for asking for asylum. So to be "afraid to participate in protests because of fear of persecution" is not enough to claim refugee status.
To elsewhere in the world, not all are legal refugees. De-facto refugees from Ukraine and Russia could leave in preceding years and did so legally. Many would be disinclined to go back since the likelihood of death or imprisonment has risen dramatically. They would be renewing their passports via embassies while working towards obtaining long-term resident status in meantime. The easiest way of obtaining that status may or may not be by asking for asylum, but regardless if you insist that guaranteed by law political persecution is not grounds for becoming a refugee I am not taking that seriously until you provide proof that reality contradicts the dictionary definition of the word.