MultiplayerSynchronizer: adding duplicate properties makes editor unresponsive

### Tested versions

4.3.stable.official

### System information

Godot v4.3.stable - Windows 10.0.19045 - Vulkan (Forward+) - dedicated NVIDIA GeForce RTX 3080 Laptop GPU (NVIDIA; 32.0.15.7216) - Intel(R) Core(TM) i7-10870H CPU @ 2.20GHz (16 Threads)

### Issue description

When adding a property to MultiplayerSynchronizer via replication tab, if that property already exists, the next time you try to add a new property editor freezes and becomes unresponsive.

### Steps to reproduce

Just try to add position property to any multiplayer synchronizer in node_3d scene, try to add it again, then open adding window again.

### Minimal reproduction project (MRP)

[reproduction.zip](https://github.com/user-attachments/files/18675172/reproduction.zip)

Start with the MultiplayerSynchronizer replication tab and the provided reproduction.zip project. Reproduce the duplicate position-property sequence, then trace the editor path used to add replicated properties; done means reopening the add-property window remains responsive after a duplicate is attempted.

Written by the indexing model from the issue text.