Hi,
Is this a new to you recently purchased outboard?
The green light not being on while running would be of great concern to me. That light indicates oil pressure is above minimum. While it could very well be a bad OP switch , electrical wiring issue, or the lamp itself causing it not to be illuminated, I would check the oil pressure before running it any longer.
Was the engine overheated at some point? Was that the reason for the waterpump being replaced?
I don't have SI for this outboard but I'm fairly confident that you can verify oil pressure via the OP switch orifice. It takes an adapter that you can get on Amazon to hook up a gauge. British pipe thread.
I will look up specifics on the pressure and adapter for you if you're not working with a manual.
As far as the poor running off of idle, the CDI has engine protection built in and will de-rate the power significantly if low oil pressure is detected. That's one possibility here.
Another, at the tip-top of the list, is that these carbs can be VERY difficult to get cleaned correctly and you probably wouldn't even be 1,000,000th guy that didn't get it right the first go-round. I'm old so I was probably the 500,000th and I would probably get it wrong every once in awhile still.
I always recommend the Honda Marine Carburetion Manual for newcomers because it can help significantly. I had rebuilt carbs for 30 years before I was turned on to that manual by the best Honda tech I've ever encountered. I bought it because HE used it. But that's 40 something $cocos$ many don't want to "invest".
Good luck.