Chain skipping?

I got a relatively new bike and I noticed the chain skips occasionally when starting up (from a traffic light stop) or when skidding (more often when I try to skid to the least comfortable side, I'm not an ambidextrous skidder but trying to learn).
I cleaned my chain thoroughly and tensioned it, there is a tiny bit of play but it is tight at the tightest spot and still get occasional skipping.
Could someone please help me diagnose the problem?
Using Alpine chainring and cog 47/17 and Izumi super tough chain. I got a parktool chain checker and the chain has not stretched.

Thanks.

check the links, you might have a tight one where it has been joined in the past
little side to side action at the tight link would free it up

I checked this video's instructions looking for a stiff link and couldn't find any https://www.youtube.com/watch?v=hklVw3KErKw

Are you sure it's the chain skipping, and not the rear cog unscrewing while skidding and then tightening again when putting power on the pedals?

I don't know, how can I tell it is the rear cog unscrewing? And how do I fix that?

I've had that before.

There's a lockring threaded on after the cog (with reverse thread) which stops the cog unscrewing. Check if it's tight up against the cog and you aren't able to unscrew it by hand

What kind of tool do I need for that?

A chain whip/lockring tool will do both your cog and the lockring

But you may be able to see if it's loose by hand. If it was moving enough to feel like it's slipping, it's probably no longer tool-tight

But first check if the cog itself is tight, because you might have unscrewed the cog tight against the lock ring while skidding. Then the lock ring seems tight, even though the cog is not fully engaged on all the hub threads.

Does the tool above work to tighten the cog as @Tijs described and the lock ring as well?
Any videos out there explaining out to do this?

The tool above is https://www.retro-gression.com/products/shimano-tl-sr22-track-chainwhip-lockring-tool and it needs a few links added to the chain to use on my 17 teeth cog.

It doesn't need to wrap around the whole cog, just a handful of the teeth so it doesn't slip.