Even if "along the wall" counts as creating cover, I don't see why Obozaya couldn't draw a line to either of the ksarik's left corners...
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"If any line from this corner to any corner of the target’s
square passes through a square or border that blocks line of effect or provides cover, or through a square occupied by a creature, the
target has cover." - Description of cover.
"If any line from this corner to any one corner of the target’s
square passes through a square or border that blocks line of effect or provides cover, or through a square occupied by a creature, the
target has cover." - My interpretation
Basically you have to choose one of your corners and be able to draw an uninterrupted line between that corner and all of the enemies corners, and if you can't there is cover between you and the enemy.
"Obozaya is adjacent to the ksarik, but
lines from every corner of her square to
all the corners of the ksarik’s square pass
through or run along the border of a wall.
The ksarik has cover from her, and she has
cover from it."-Excerpt from the example of cover from CRB.
This supports my interpretation, and yes, the line running along the border of a wall counts as interrupted.
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The ksarik has cover because they're on opposite sides of the line.
No, this isn't spelled out anywhere explicitly. Yes, it sounds slightly absurd when put that clearly. But that's really what it is, and it's terribly explained. The ksarik doesn't have cover because the line shown runs along a wall; the ksarik has cover because the line runs along a wall, and Obozaya is on the 'other side.'
Consider this. Extend the wall further along the line being drawn. In the example in the CRB, this will completely block Obozaya's line of sight and line of effect. Consider doing this with your example now. What has changed? Nothing. In your hallway example, both opponents would be on the same side of the line being drawn to check for cover, and therefore it does not intersect the wall. Thus, the wall does not provide either of them cover.
I believe this is the basic, fundamental logic behind the example given in the core rulebook. I don't think you'll find it spelled out explicitly anywhere, nor will you readily find a more eloquent explanation. But that's what it is.
I think this makes some sense when you actually stop and consider it. But they also should have actually explained this detail, given the examples they chose.
Since partial cover exists, why isnt it partial cover in this example?
Partial Cover
If more than half of you is visible, your bonuses from cover are
reduced to +2 to AC and +1 to Reflex saving throws.