How to achive infinite zoom for Mandelbrot set depictions with WebGPU?

Question

I see that this question is quite popular, but I couldn't find one in the context of WebGPU.

This is the shader code I wrote for rendering the Mandelbrot set.

@vertex
fn vert_main(@location(0) pos: vec2<f32>) -> @builtin(position) vec4<f32> {
    return (vec4<f32>(pos, 0, 1));
}

struct Input {
    dummy: f32,       // Ignore this
    scalar: f32,      // The zoom level
    center: vec2<f32> // The origin point on the canvas
}

const colorCount = 500;
const maxIterations = 1000;

@group(0) @binding(0) var<uniform> inputs: Input;
@group(0) @binding(1) var<uniform> colors: array<vec4<f32>, colorCount>;

@fragment
fn frag_main(@builtin(position) fragCoord: vec4<f32>) -> @location(0) vec4<f32> {
    let C = (fragCoord.xy - inputs.center) * inputs.scalar;
    return colors[getMandelBrotIterations(C) % colorCount];
}

fn getMandelBrotIterations(C: vec2<f32>) -> i32 {
    var Z = vec2<f32>(0.0, 0.0);

    for (var i = 0; i < maxIterations; i++) {
        Z = square(Z) + C;
        if ((Z.x * Z.x + Z.y * Z.y) >= 4) {return i;}
    }

    return 0;
}

fn square(Z: vec2<f32>) -> vec2<f32> {
    return vec2<f32>(Z.x * Z.x - Z.y * Z.y, 2 * Z.x * Z.y);
}

Apparently, this has the pixelation issue on zooming due to limited precision. I think even if there was a float64 type in WebGPU, the issue is still bound to happen at one point. So, what's the strategy behind achieving the infinite zoom as seen in those YouTube videos?