These 4 scripts make the Timeline able to handle Gameobject's parenting

SetParentBehaviour.cs

using UnityEngine;
using UnityEngine.Playables;

public class SetParentBehaviour : PlayableBehaviour
{
    public Transform parentObject;

    public override void ProcessFrame(Playable playable, FrameData info, object playerData)
    {
        if (parentObject == null) return;

        var transform = playerData as Transform;
        if (transform != null)
        {
            transform.SetParent(parentObject, true);
        }
    }
}

SetParentClip.cs

using UnityEngine;
using UnityEngine.Playables;
using UnityEngine.Timeline;


public class SetParentClip : PlayableAsset, ITimelineClipAsset
{
    public ExposedReference<Transform> parentObject;
    public ClipCaps clipCaps => ClipCaps.None;

    public override Playable CreatePlayable(PlayableGraph graph, GameObject go)
    {
        var playable = ScriptPlayable<SetParentBehaviour>.Create(graph);
        var behaviour = playable.GetBehaviour();
        behaviour.parentObject = parentObject.Resolve(graph.GetResolver());
        return playable;
    }
}

SetParentMixerBehaviour.cs

using UnityEngine.Playables;
using UnityEngine;

public class SetParentMixerBehaviour : PlayableBehaviour
{
    public Transform defaultParent;
    public override void ProcessFrame(Playable playable, FrameData info, object playerData)
    {
        int inputCount = playable.GetInputCount();
        Transform bindedTransform = playerData as Transform;
        bool clipFound = false;

        for (int i = 0; i < inputCount; i++)
        {
            float inputWeight = playable.GetInputWeight(i);
            ScriptPlayable<SetParentBehaviour> inputPlayable = (ScriptPlayable<SetParentBehaviour>)playable.GetInput(i);
            SetParentBehaviour inputBehaviour = inputPlayable.GetBehaviour();

            if (inputWeight > 0.5f)
            {
                clipFound = true;
                inputBehaviour.ProcessFrame(playable, info, bindedTransform);
            }
        }

        if (!clipFound && bindedTransform != null)
        {
            bindedTransform.SetParent(defaultParent, true);
        }
    }
}

SetParentTrack.cs

using UnityEngine;
using UnityEngine.Playables;
using UnityEngine.Timeline;

[TrackColor(0.855f, 0.8623f, 0.87f)]
[TrackClipType(typeof(SetParentClip))]
[TrackBindingType(typeof(Transform))]
public class SetParentTrack : TrackAsset
{
    public ExposedReference<Transform> defaultParent; // Parent par défaut à utiliser lorsque aucun clip n'est trouvé

    public override Playable CreateTrackMixer(PlayableGraph graph, GameObject go, int inputCount)
    {
        var mixerPlayable = ScriptPlayable<SetParentMixerBehaviour>.Create(graph, inputCount);
        var mixerBehaviour = mixerPlayable.GetBehaviour();
        mixerBehaviour.defaultParent = defaultParent.Resolve(graph.GetResolver());
        return mixerPlayable;
    }
}