Sorry, I didn't get any notifications of new posts...
As Mike said, the solenoid, when activated with 12 volts (crank/run) opens and allows fuel to flow.
Here is your engine's parts diagram:
https://jackssmallengines.com/jacks-parts-lookup/manufacturer/briggs-stratton/briggs-stratton-engine/200000-399999-series/33r800-to-33r899/33r877-0004-g1 As Mike said, the main jet can screw in or be "set" in place.
There's 2 carbs available for you engine. The Ruixing or the NIKKI (see diagram on above link).
The solenoid just screws into the bottom of the float bowl. If they sit a long time, they can get stuck
in the closed/extended position. If any doubt, I remove the solenoid and cut off the pin that extends(and stops fuel) from flowing.. The solenoid now doesn't need power/can't go bad as you
removed the pin... As long as the carb float/needle are properly working, it won't hurt anything.
The Ruixing is the basic/ built like most carbs.
The NIKKI, IME, is junk. The large plastic part that holds the float/needle/jet (jet is stuck right down the middle) uses a funky "gasket". Some NIKKIs have a separate o -ring that goes bad, leaks or just doesn't seal...
Did you re-set the governor with the carb?
.
Scott