It’s very normal for them to fidget and grunt and things in their sleep at this age. You could try white noise as it helps settle baby but also helped me and my husband sleep through the grunting! I still woke when I needed to/when baby cried x
My four week old does that too. She's doesn't move quite as much as in your video, but she makes all those noises, and so loudly! We moved her into her own room at three weeks because of it. I know that's not recommended, but it's worked for us. We're all sleeping better, her included, as we're no longer constantly going to her thinking that she wants soothing when really she's perfectly happy asleep, just grunting.
I would definitely advise swaddling as their startle reflex can shock them into waking but the grunting noises could be down to gas or even a bit of reflux especially if he’s feeding close to bed time, maybe try a cot wedge, it elevates them to a slightly raised level which is fine for sleeping as essentially their still laid flat but the angle can help them bring up gas during the night a little easier and also prevent reflux if that’s travelling up when laid completely flat out my dd was the same, we used to let her on her side (not everyone’s agreed) but she enjoyed that and even now at 6mo she makes the odd grunt but not as many since we got the wedgehog!
Our almost 4 week old does this. With him, it's almost certainly st least partly wind - gut wind, not burps. He wriggles and grunts and farts all night! He seems to sleep through it most the time though, it just wakes me up!! We've started him on Infacol although not sure if it's helping yet
My 5 week old is the same. He suffers with wind a lot and also had infant gaviscon for reflux. He still does it even after having the dentinox and gaviscon. My daughter was the same and it just got better with age x