Mercury 9.9 4 stroke does not hold idle position

First of all I apologize if this is a naive/stupid question... I am a new boater with not much experience... I have a 9.9hp 4 stroke Mercury outboard bought new last winter that I used all season and the dealer winterized at the end of the season. I started it for the 1st time this year and it fired up after a few pulls, smoked and then I run fine it for a few minutes but whenever I pushed the choke back or reduced the rpm it shut off. After trying again a few times it consistently does not hold the idle position and dies. For the few seconds on idle I can keep it does not sound as smooth as it did last year.
I am guessing maybe the carburetor is dirty and does not suck up fuel as it should? The fuel was stabilized with an additive at the time of winterization so I suppose it should be good. The fuel demand valve next to the tank is only 1 year old so I assume it does not come from there either. Is there any easy test I could do to see where the issue comes from without having to take the whole carburetor out and open it? Maybe I can just play a bit with the oxygen/fuel ratio screw to see if it can make it run smoother at idle?
I would appreciate your thoughts on that.
Thanks!

I had that exact motor (mine was a 2004) with the exact same problem

there was a small bit of plugging in the carb

What it did (I do this on small motors sometimes when they act strange) is start it in your driveway with water connected to it, let it warm up

Then, give it full throttle and while it is revving up put the palm of your hand tight over the air intake of the carb. Just do this briefly, it will create a ton of vacuum in the carb and if you are lucky it will clean out the passage that is plugged.

This worked for me after a few attempts. Its just an old trick we use on small motors.

Might not help but its worth a try

Ok so after a few more tests it now does hold idle but when I increase the rpm continuously I hear the engine make more noise then much lower (almost as if would stop) then back up again. I don't recall seeing that before but maybe I disn't pay too much attention, I don't know... Does it ring a bell?
Pechjerker, where do I find the air intake of the carb?

the big round hole in front if the carb that air gets sucked into. the choke plate is in there

sometimes its called the air horn.

ok so I ended up having a carb rebuild done, everything seems fine now (fingers crossed until I test it on the water and not only in the driveway...).