It sounds like a fuel flow issue. You may have some schumtz in the inlet pipe or down around the shutoff valve of the sediment bowl.
If you disconnect the input side of the add on filter and let gas run into a container how strong of a flow do you get? Good steady pencil lead sized stream for 20-30 seconds is what you're looking for. If you get that, the problem is farther downstream. Less than that, and it's upstream (Which is where I'm betting it is by what you've said). Use a clean container and you can dump the gas back in the tank.
If it's upstream it's not real easy but you can remove the sediment bowl (just the glass) and hold a cereal bowl sized container under it and open the valve to see how well it flows. It should squirt out sideways on two sides. There's a little disc in the end of the stem hanging down into the sediment bowl. Poke a wire in from the side and up the tube, be ready for gas to flow. You can also try poking it down the tube in the gas tank through the filler hole. You wont get all the way through either way because of the valve.
If it's downstream connect up your filter and pull the plug on the bottom of the carb, do you get a good pencil lead sized stream for 20-30 seconds? Yes, then it's in the carb. No, then disconnect the line coming into the carb and try again. Good flow there means it's either the inlet screen on the carb or the needle/float is sticking. Bad flow there means get rid of your add on filter and try again.
Two points just to clarify operation, nothing is getting pulled, it's all gravity flow. The choke position has no relationship to how much gas will flow. The choke position will affect how much/little air mixes with the available gas to get it to the right proportions to burn.
Welcome to the forum!