Significant pause in sync when switching MultiplayerSynchronizer's authority

[romlok]

Godot version

v4.1.2.stable.official [399c9dc]

System information

Godot v4.1.2.stable - Debian GNU/Linux trixie/sid trixie - X11 - Vulkan (Mobile) - dedicated NVIDIA GeForce GTX 1060 (nvidia) - Intel(R) Core(TM) i5-8400 CPU @ 2.80GHz (6 Threads)

Issue description

When the authority for a MultiplayerSynchronizer is changed from one peer to another, there is a significant and noticeable delay (I've seen up to several tens of seconds) before synchronisation with the new authority begins.

Note this appears to only be the case when using the sync mode. If a property is watched, there is no perceptible delay.

Steps to reproduce

1. Run 3+ copies of the attached scene

2. In one instance, click "Host" to start the localhost server
   

3. In the other instances, "Join" the server

4. Clients: Select a different type of sprite motion for each client instance
   

5. Host: Use the "Authority" buttons on the server to change the MultiplayerSynchronizer authority between the peers:
   

6. Host: ⚠️ Observe that every authority change after the first will cause the sprite to immediately stop moving, before resuming some seconds later with the new authority's movement ⚠️

7. In the editor, change the MultiplayerSynchronizer's replication mode for the sprite's position from Sync to Watch
   

8. Host: Observe that there is no longer a delay when switching authority.

Minimal reproduction project

Single self-contained scene file:
authority_switcheroonie.zip

[Calinou]

cc @Faless