This is purely an animation issue. A typical "knee pop" we get when animating legs in IK incorrectly.
Enabling motions paths on the knee and feet from the Armature Properties > Motion Paths panel allows you to track the location of the different joints through time and better understand what's going on:
You can also use the annotation tool to trace over the animation and analyze what the limbs do:
The issue is that you have several frames where the knee is either too close or backtracking from its position in the previous frame.
Such as here:
So you have to modify the poses to correctly transition from the different movements.
We can see at frame 19 the foot is placed perfectly between two keyframes by the interpolation, but what you need is pull out the foot a bit further. You can also look at the knee angle and consider that it wouldn't go from a fully extended leg to an almost half bent leg in two frames, and then unbend and bend again before the foot goes down under the body again. You need to pay attention to how the movements transition from and towards each other.
Furthermore, you also need to pay attention to the spacing of each frame. When the foot and knee reach the apex of their back movement, they decelerate, and then accelerate when going forward again to make a new step. This should be visible in the spacing that should be tighter in the apex.
It also doesn't help that your hips do not participate in the motion. They should pitch, yaw and roll to both accompany the legs movement and counterbalance the weight. And the whole spine should be affected up to the head too. Without hip rotations, you end up having less options for things such as how to extend legs to have your knee - foot timing and spacing correct.
To be honest, this kind of tight-knit animations rarely ever have any frame left to interpolation, everything gets hand keyed precisely to avoid these kinds of issues.
And while using FK instead of IK usually makes this issue less frequent to happen, it usually trades it for others, such as handling ground contact in FK being a pain, or alternating between FK and IK depending on whether the foot is in contact with the ground. And in any case, it although each solution has its advantages and inconveniences depending on the scenario, the basics of timing x spacing and other animation principles are always to be kept in check.
With just a quit retouch on one foot ik controller trying to touch up the timing and spacing, here's what you can get already:
I highly recommend you to take a look at the run cycle sheets from the Animator's Survival Kit by Richard Williams (or even get the book altogether, it's a goldmine for animators).
