MN gets very extreme over things like this. Do hide the thread if you need to take a break.
FWIW - my youngest, not quite 4, would not do this. The older two, at that age, I don't know if I could have trusted them not to. I REALLY don't think this is a universal thing where all 4 year olds are exactly the same. And even when it is something you generally trust them not to do, I've definitely had moments with all the kids - I remember going into DS1's room when he was 6 and he had inexplicably drawn on the carpet with felt pen. It was a rented house and I have no idea why he did it because he was perfectly fine with pens 100% of the rest of the time. The funny thing was even he couldn't answer why he'd done it!
Secondly, it's totally fine to be angry, hurt, upset by things that happen even if they have happened because it was a child being impulsive and not malicious. It's totally normal and human to have emotions. It wouldn't be fine if e.g. you went full on hulk and destroyed his posessions in retaliation, or banned him from birthday parties for a year or something equally unhinged, but you didn't do that. You probably had a totally understandable emotional outburst on first discovering the presents and then decided on a reasonable consequence or future management strategy (if it even needed either) when feeling calmer. It's totally fine and normal to need some space and be pissed off. Finding it hard to look at him doesn't mean not looking at him, and is not at all the same thing as manipulatively performing some kind of silent treatment/rejection as a punishment. Some posters really like to project their own abusive childhoods on here, and I'm sorry for anyone who has experienced it, but it's not the same thing as a parent who is struggling to process something that has happened, especially when it's tied to something of high emotional significance e.g. a birthday.
I've seen a bit of discussion online about how we seem to have this idea now that being mentally healthy means being perfectly happy and calm at all times, but in reality it is normal to experience anger, upset, sadness, regret, disappointment etc. It's also OK if those feelings last longer in response to "bigger" events, it doesn't mean there's anything wrong. I expect all you need OP is a bit of time and you'll feel better and, like people said at first, in a few years it will have faded to just be a funny story.