class definition and problem with a method

[HerrAyas]

Hi all,
I am trying to understand the correct usage of classes and methods (== functions inside the class definition?)
Below you see a class "Punkt", which refers to points in a 2D-plane with an x and y coordinate.
Simple enough, I try to add two points p1 and p2
First try: p1+p2 --> "unsupported operand type" (understood)
2nd try: Write a function "add" wich manipulates the .x and .y properties of the object "Punkt"
3rd try: Implement the function in the class definition (is that called "method"?) Here's the code:

class Punkt():
    def __init__(self, x = 99, y = 99):      #ALWAYS give default-values!
        self.x = x
        self.y = y

    def __str__(self):
        return f'( {self.x} | {self.y} )'
    
    def add(self, p1, p2):
        self = Punkt()             #WHY? WITH this line, every result is 99/99 
        self.x = p1.x + p2.x
        self.y = p1.y + p2.y
        return(self)
    
p1 = Punkt()                    #without __init (x and y defaults) here's an error
p1.x = 17                       #without __init (complete) no one has a problem
p1.y = 12

p2 = Punkt(-9,-4)

p3 = Punkt()
p3.add(p1,p2)                
print(f"Punkt 1: {p1}")
print(f"Punkt 2: {p2}")
print(f"Punkt 3: {p3}")

In line 10 you see me trying to initiate an object "Punkt" called "self", so I have something to work with.
But if I do so, the output of "print Punkt 3 {p3}" is always the default value of 99/99.
I thought, self = Punkt() calls an object called "self", which is a "Punkt()" and has the default values of x=99 and y=99.
After that, (line 11/12), I manipulate the self.x and self.y and return the new, edited values.

I tried much and over and over - just accidentially put a # in front of line 10 "self = Punkt()" and BOOM - it worked.

It would be very nice, if somebody could explain this to me (in simple words - kind of new to python :)

Greetings,
MrAyas

Output WITH line 10 active

Output:
Punkt 1: ( 17 | 12 )
Punkt 2: ( -9 | -4 )
Punkt 3: ( 99 | 99 )

Output WITHOUT line 10

Output:
Punkt 1: ( 17 | 12 )
Punkt 2: ( -9 | -4 )
Punkt 3: ( 8 | 8 )