Assume true. What would Putin say or do to this soldier if they were to meet? Publicly? Privately?
Assume a Ukrainian soldier has done the same. What would Zelenskyy say or do to his soldier? Publicly? Privately?

Think about those for a while. What will people of all priorities (pro-Russia, pro-Ukraine, anti-conflict, etc.) think about the decisions that are made and things that are said?

I don't have the answers to these questions, but know what my guesses would be and I can see people of either side of this conflict giving any one of the possible answers and justifying it either way.

e.g. Imagine Putin has his soldier court-martialled and shot; Some pro-Russians will proclaim this a strong move. Others will say that he should not have done that because those Ukrainians deserved to be murdered and the soldier did the right thing. Likewise if Putin was to throw this soldier in prison, some might say it wasn't enough and others might say that he shouldn't even be in there. (NB: I don't believe anyone deserves to be murdered. Ukrainian or Russian. This is all hypothetical.)

Alternatively, we might have Putin outwardly congratulate this soldier. This would be an internationally unpopular move, more-so than having the soldier shot, because the West kind of expects Putin to "deal with" people who make him look bad, but some pro-Russians would proclaim it a strong move. Others will think that it was a bad idea but say nothing.

Zelenskyy might have his own soldier court-martialled and shot. If he is truly interested in aligning with the West as Russia fears, he probably wouldn't do this. He'd instead have the soldier tried in court, and if found guilty, possibly even turned over to Russia if it could be guaranteed the soldier was going to be imprisoned for his crimes and not tortured or shot.

Would Russia consider turning over their own POW murderers to Ukraine? Probably not. They don't recognise Ukraine.

It would be nice if they did though. If they realised where their soldiers and tanks were they might be able to get them out of there and this conflict would be over. Enough lives have been lost to make up for any transgressions either way at this point.