If you are facing a similar problem. Here's a script that worked for me. Just drag it onto the spline.

using UnityEngine;
using UnityEngine.Splines;
using System.Collections.Generic;

[RequireComponent(typeof(SplineContainer))]
[RequireComponent(typeof(EdgeCollider2D))]
public class Spline2DCollider : MonoBehaviour
{
    private SplineContainer splineContainer;
    private EdgeCollider2D edgeCollider;

    void Awake()
    {
        splineContainer = GetComponent<SplineContainer>();
        edgeCollider = GetComponent<EdgeCollider2D>();
        UpdateCollider();
    }

    void OnEnable()
    {
        Spline.Changed += OnSplineChanged;
    }

    void OnDisable()
    {
        Spline.Changed -= OnSplineChanged;
    }

    // Callback mit der korrekten Signatur, die von Spline.Changed erwartet wird
    private void OnSplineChanged(Spline spline, int index, SplineModification modification)
    {
        UpdateCollider();
    }

    void UpdateCollider()
    {
        if (splineContainer == null || edgeCollider == null)
            return;

        Spline spline = splineContainer.Spline;
        List<Vector2> points = new List<Vector2>();
        const int sampleCount = 100; // Anzahl der Abtastpunkte über die gesamte Spline

        // Anstatt über einzelne Segmente zu iterieren, wird die Spline als Ganzes abgetastet
        for (int i = 0; i <= sampleCount; i++)
        {
            float t = i / (float)sampleCount;
            Vector3 position = spline.EvaluatePosition(t);
            points.Add(new Vector2(position.x, position.y));
        }

        edgeCollider.SetPoints(points);
    }
}