Can you post the model, type and code please aldot?
It is a governed idle engine, so it has no idle speed screw. The small governor spring essentially controls the idle speed, and the larger spring controls the speed from there on up to maximum speed. Maximum speed is normally 3000 rpm for vertical crankshaft engines, but may be 3500 for horizontal crankshaft engines. The reason for this difference mainly relates to US blade-tip speed restrictions in the US. Idle speed is usually 1750 rpm for Briggs small vertical crankshaft engines.
The engine speed in air vane governed engines such as that is determined by a tug of war between the air vane and the governor spring. The faster the engine runs, the harder the air vane tries to close the throttle. The more you stretch the governor spring (by moving the speed control toward high speed) the harder the spring tries to open the throttle. The vane and spring find an equilibrium speed that is almost unaffected by the load on the engine. Note that the speed depends only on the governor spring's characteristics, its amount of stretch set by the speed control lever, and the governor vane's characteristics. The speed is not affected by the length of the governor wire link. Essentially, the design engineer puts the vane, the carburetor's throttle butterfly, and the speed control lever where he must, then designs the governor spring, and the location of the loop in the governor wire link, to give the required speed range.
The idle speed is determined by the air vane and the idle speed spring, and is set by bending the stationary tab to the right of your thumb in the last picture. The main governor spring should be more or less relaxed at idle, so it should not have much influence on the idle speed.
To find out why your idle speed is way too high, you might try removing the idle spring and checking the idle speed. It should be approximately zero. If the engine still idles briskly without the idle spring, you have either the wrong main governor spring, or a mechanical foul up in the governor linkage. It might be some jamming in the vane, the link, or the link's pivots at the vane and the throttle butterfly. However my first guess would be that you have the main governor spring installed backwards, so the coiled part is hitting the throttle butterfly bell crank, instead of the straight end of the spring sliding easily over it. I'd like to pretend that I got this idea just because I'm intensely familiar with that governor, but in reality I took a look at the diagram in the Briggs manual:
Post-edit: Looks as if we both figured out the same solution at the same time, Aldo. Just check if the coiled part of the spring is hitting the butterfly bell crank.