Couple hints about genny fuel system:
I cannot tell for sure by looking at your pic's, but usually on Honda's and other small gen's especially with a on top gas tank there is a petcock on the bottom of the tank and on the end of the petcock up inside the tank is a pre-filter screen and also if the petcock is kind that can be taken apart their is a additional finer screen inside the petcock assembly and they will get restricted and the gen will starve for fuel.
Sometimes you can pull the fuel line off at the carb and the fuel line will flow gas good for awhile and then slow down.
Engine will start and run for awhile after it's rested.
You can remove the gas cap and blow low pressure air, about 3 lbs back through the fuel line to the petcock and up into the gas tank and
momentarily clear/backflush the screen in an emergency situation, even use your mouth to blow backwards, but this is only temporary because you push the gunk back into the gas tank. The on top gas tanks have a low sump so as to burn the last of the gas in the tank and the low portion at the petcock is also where trash settles.
You will have to drain and remove the tank and give it a good cleaning and the pre-screen filters
AND for a in-line fuel filter for Gravity fed gas systems (no fuel pump) you should be using the Briggs RED 150 micron fuel filter.
The WHITE finer 75 micron fuel filter is to fine for gravity fed fuel and the engine may starve for fuel.
If you find good filters in the petcock and fuel tank you can remove your fuel filter or use the Briggs RED. Do not try the flea bay Clone aftermarket Red filters, they are POS and will eventually leak at their seams. NAPA has the good red ones also.
AND it appears that your fuel filter is the clear plastic type and I've seen engines operate ok and that type filter and show very little visible fuel inside, making one think that fuel flow is a problem.