Webeditor does not display `(Re)Importing Assets` dialog

### Tested versions

4.7.stable

### System information

Godot v4.7.stable - Web - Single-window, 1 monitor - OpenGL ES 3 (Compatibility) - ANGLE (AMD, Radeon R9 200 Series Direct3D11 vs_5_0 ps_5_0), or similar - (2 threads) - AudioWorklet (48000 Hz, Stereo/mono)

### Issue description

Webeditor does not display `(Re)Importing Assets` dialog when importing textures.

This is especially problematic when opening a project the first time as the editor will freeze during the import, but the user will not understand why.

### Steps to reproduce

In the WebEditor, select the icon.svg file and press the Reimport button in the Import panel. Note how no popup appears as it reimports.

### Minimal reproduction project (MRP)

NA

Start by reproducing the issue in the WebEditor with icon.svg: select it in the Import panel and press Reimport while observing the missing dialog and editor freeze. Trace the WebEditor import flow and compare it with the non-Web behavior; done means the `(Re)Importing Assets` dialog appears during texture importing and explains the initial import delay.

Written by the indexing model from the issue text.