Profiler hangs

### Tested versions

V4.2.1 stable b09f793f5

### System information

Godot v4.2.1.stable - Ubuntu 23.04 23.04 - X11 - Vulkan (Forward+) - dedicated NVIDIA GeForce GTX 1060 6GB (nvidia; 535.146.02) - AMD Ryzen 5 2600X Six-Core Processor (12 Threads)

### Issue description

When profiling particularly slow code, the profiler hangs, the graph shrinks as to indicate a huge peak but fails to show said huge peak.

The game instance continues to run albeit at very reduced frame-rate, inputs are not handled. Including window buttons.

I would expect that profiling would work normally, a gigantic 6000ms or so peak appearing and game execution continuing as normal.

### Steps to reproduce

Have a large project with a large convoluted procedural level generator written in GDscript.
Attempt to profile it

### Minimal reproduction project (MRP)

N/A

Start by reproducing the hang in Godot v4.2.1 on Ubuntu with a large project using a convoluted procedural level generator written in GDScript. Compare the profiler graph and game responsiveness during the slow code; done means the large peak is shown and the profiled game continues handling input normally.

Written by the indexing model from the issue text.