Confusing behavior of the run project buttons when using Profiler

### Tested versions

Reproducible: at least from v4.5.1.stable.official [f62fdbde1] through v4.7.dev.custom_build [a9afde840].

### System information

Godot v4.7.dev (a9afde840) - Windows 10 (build 19045) - Multi-window, 1 monitor - Vulkan (Forward+) - dedicated NVIDIA GeForce RTX 3050 Ti Laptop GPU (NVIDIA; 32.0.15.8183) - AMD Ryzen 5 5600H with Radeon Graphics (12 threads) - 15.34 GiB memory

### Issue description

When you click on the Profiler graph the game pauses. To unpause the game you should press the PAUSE button again which is highlighted blue. If you press the PLAY button it will close or re-run your game.

https://github.com/user-attachments/assets/3d82bd59-e197-4ee5-b2e1-dbc31649d191

### Steps to reproduce

1. Start profiling and click on the Profiler graph.
2. Try to unpause using the PLAY button.

### Minimal reproduction project (MRP)

N/A

Start by reproducing the behavior from the Profiler graph and the PLAY and PAUSE buttons using the listed steps. Trace how clicking the graph changes the running state and how each button is presented or handled; done means the controls clearly indicate the correct action and PLAY does not unexpectedly close or rerun the game when unpausing.

Written by the indexing model from the issue text.