WebGL build fails with “Internal build system” error when "Name Files As Hashes" is enabled

How to reproduce:
1. Open the “WebGL_Hashes_Bug“ project
2. Switch to WebGL Platform (File > Build Settings)
3. Build the project with all 7 scenes
4. Observe the Console

How to reproduce in a new project:
1. Create a new project with the “3D Core” template
2. Switch to WebGL Platform (File > Build Settings)
3. Select “Add Open Scene”
4. Enable “Name Files As Hashes” (File > Build Settings > Player Settings > Publishing Settings)
5. Build the project
6. Observe the Console

Expected result: project builds successfully
Actual result: “Internal build system” error is thrown and the project fails to build

Reproduced with: 2022.2.19f1, 2022.3.1f1
Not reproduced with: 2021.3.27f1, 2022.2.18f1, 2023.1.0b20, 2023.2.0a18

Reproduced on: Windows 10 (by reporter), Windows 11

Error logged to the Console when failing to build:

Internal build system error. Backend has requested a buildprogram run 6 times.
UnityEngine.GUIUtility:ProcessEvent (int,intptr,bool&)