Project manager not applying custom theme correctly

### Tested versions

Reproducible in: 4.3 dev 3 [36e943b6b] and above. - Not reproducible in 4.3 dev 2 [352434668] and below

### System information

Godot v4.3.stable.mono - Windows 10.0.19043 - Vulkan (Forward+) - dedicated NVIDIA GeForce GTX 750 Ti (NVIDIA; 31.0.15.3734) - AMD Ryzen 5 2600 Six-Core Processor (6 Threads)

### Issue description

The project manager UI (specifically the bit where you can scroll between projects) doesn't apply custom themes properly, instead it shows the last selected built-in theme, so if i select the default theme and then my custom theme i get:


if i select the black (OLED) theme and then my custom theme i get:


if i select the Godot 2 theme and then my custom theme i get:


so on and so forth...
As you can see this didn't happen in earlier versions like 4.2.2, where that area is consistent with the rest of the UI:


This bug seems to have been introduced in 4.3 dev 3, as 4.3 dev 2 and previous versions don't show signs of having this bug

4.3 dev 3:


4.3 dev 2:


### Steps to reproduce

Create a custom theme, select the default theme and then the custom theme, open a new instance of Godot (thefore opening the project manager). You should now see that area in the UI display the default theme instead of the custom theme.

### Minimal reproduction project (MRP)

[project-manager-theme-bug.zip](https://github.com/user-attachments/files/16735383/project-manager-theme-bug.zip)

Start by reproducing the issue in Godot 4.3 dev 3 or later using the attached project-manager-theme-bug.zip, switching from the default theme to a custom theme before opening the project manager. Trace the project manager's theme handling and compare it with 4.3 dev 2; done means the scrollable project area consistently displays the selected custom theme.

Written by the indexing model from the issue text.