Toilet fails to refill after flush, please help! With pictures

So I'm a first time home owner and I've got some minor repairs that I'd like to take care of. After some fiddling around and some basic research of how toilets work I still can't find exactly what I'm looking for so joined up in the hopes that someone here might know what I need to adjust or fix.

Basically my toilet fails to refill all the way when I flush it, causing it to not refill enough for a second flush if need be. Here are pictures before and after flush.

Before:


After


If I simply lift up on the black lever (circled in red) the bowl begins to refill without an issue.


I had tried twisting the refill float attached to the black lever down and up but that seems to just control the water level in the tank. I would presume that I need the water to lift the refill valve up high enough for it to initiate and cause the bowl to refill, but what do I need to adjust to make this happen.

Any help would be greatly appreciated.
Thanks!

The Fluidmaster fill valve needs to be adjusted higher to begin with.

There is a collar near the bottom, that if slid up, allows the entire assemble to be lifted higher.
When you have it where it should be, you can push the collar down to hold it in place.

Make sure you have the water off first.