Deployment of leading or trailing edge flaps - increase or decrease the angle of attack and critical angle of attack?
How does AOA change?
The angle of attack (AOA) is defined as as the angle between the chord line and the relative wind. When flaps and slats are deployed, the effective chord line changes. This is already nicely illustrated for trailing edge flaps in the article you linked:

(boldmethod.com)
As you can see, the new chord line has a higher angle compared to the relative wind, which results in an increase of AOA. Combined with the increase in camber, this will result in more lift (at the same airspeed), which means the pilot will usually reduce pitch to lower the AOA again when flaps are deployed.
I modified this image to illustrate the same for slats:

Now the new chord line is at a slightly lower angle compared to the relative wind, which results in a reduced AOA. The same is true for other leading edge devices (like e.g. Krueger flaps).
How does critical AOA change?
This depends on the exact type of device used. The following graphic shows how the coefficient of lift $C_L$ as a function of AOA $\alpha$ changes with various trailing edge high lift devices:

(HAW Hamburg - Aircraft Design)
For the slotted flap, critical AOA remains unchanged, but for all other types shown here critical AOA is reduced when deploying flaps. Note however that the maximum lift coefficient is always higher. The reason for the change in slope for extending flaps is already explained here: Why does lift curve slope increase when Fowler Flaps are deployed?.
The following graphic shows the same for leading edge high lift devices:

(HAW Hamburg - Aircraft Design)
Here, critical AOA is always increased compared to the clean wing.