Rotation inside MeshInstance3D surface plane

Question

I'm trying to make a representation of a plane that rotates around a hole in a MeshInstance3D.

So far I've managed to make the circle's hole, but I can't make the plane rotate around the hole. (The hole can't rotate, just the plane)

Here is what I have now:

extends MeshInstance3D

@export var xSize = 20
@export var zSize = 20

@export var update = false
@export var clear_vert_vis = false
var speed = 0.0001

# Called when the node enters the scene tree for the first time.
func _ready():
    #generate_terrain(speed : float)
    pass # Replace with function body.

func generate_terrain(speed : float):
    var a_mesh: ArrayMesh
    var surftool = SurfaceTool.new()
    
    var n = FastNoiseLite.new()
    
    n.noise_type = FastNoiseLite.TYPE_PERLIN
    n.frequency = 0.1 * speed
    
    
    
    surftool.begin(Mesh.PRIMITIVE_TRIANGLES)
    
    
    
    for z in range(zSize +1):
        for x in range(xSize+1):
            var y_variation = cos(speed)
            var y = 0 #n.get_noise_2d(x*0.5,z*0.5) * 4* y_variation
            
            var x1 = x -xSize/2
            var z1 = z -zSize/2
            
            if inside_circle(xSize/2,x, z, 4):
                y = speed * -1
                pass
            elif around_circle(xSize/2, x, z , 4, 8):
                y = n.get_noise_2d(x*0.5,z*0.5) * 4* y_variation
                var angle = int(speed) % 90
                
                # x1 and z1 should rotate around center
                #x1 = cos(angle)
                #z1 = sin(angle)
                #rotate(Vector3(0,1,0), angle)
            
            # Place in center 0, 0
            
            # tying to make the rotation, but it is on wrong axis
            #var xNew = x1 * cos(speed) - z1 * sin(speed)
            #var zNew = x1 * sin(speed) - z1 * cos(speed)
            
            # uv
            var uv = Vector2()
            
            uv.x = inverse_lerp(0,xSize, x1)
            uv.y = inverse_lerp(0, zSize, z1)
            surftool.set_uv(uv)
            
            # vertex
            surftool.add_vertex(Vector3(x1,y,z1))
            
    
    var vert = 0
    for z in zSize:
        for x in xSize:
            surftool.add_index(vert+0)
            surftool.add_index(vert+1)
            surftool.add_index(vert+xSize+1)
            
            surftool.add_index(vert+xSize+1)
            surftool.add_index(vert+1)
            surftool.add_index(vert+xSize+2)
            vert += 1
        vert += 1
    
    surftool.generate_normals()
    
    a_mesh = surftool.commit()
    
    mesh = a_mesh
    
    
    
    pass

# return the circle around the plane
func inside_circle(center: float, x: float, z: float, radius : float):
    var dx = center - x
    var dz = center - z
    var distance_squared = dx * dx + dz * dz
    return distance_squared <= radius * radius
    enter code here

# return a ring around the circle
func around_circle(center: float, x: float, z: float, inerradius: float, radius : float):
    var dx = center - x
    var dz = center - z
    var distance_squared = dx * dx + dz * dz
    return distance_squared <= radius * radius and distance_squared > inerradius * inerradius

# Called every frame. 'delta' is the elapsed time since the previous frame.
func _process(delta):
    speed *= 1.01
    generate_terrain(speed)
        
    if clear_vert_vis:
        for i in get_children():
            i.free()
    pass

How can I make this plane rotate around the hole, without the hole rotating?