Hi.
I had a similar issue with my 2004 Mercury 15hp 2 stroke. Would not idle correctly. I ended up fitting the carb repair kit and it did sort the issue.
There are two kits available the repair kit and the gasket kit. The attached photos show what comes in each kit.
I also found that the previous owner had put the wire link for the fast idle knob in the wrong place meaning it would not work correctly.
Hope this helps and good luck [emoji6]