Materials do not transfer texture when the "Shader" parameter is changed from "Unlit/Texture" to "Universal Render Pipeline/Unlit"

Reproduction steps:
1. Open the attached “repro_IN-87030“ project
2. Open the “Assets/Test.unity“ Scene
3. Select the “Assets/New Material.mat“ material
4. In the Inspector, change the shader to “Universal Render Pipeline/Unlit“
5. Open the Game view
6. Observe the texture on the “Cube“ GameObject

Expected result: The texture remains
Actual result: The texture is removed and the “Cube“ GameObject becomes white

Reproducible with: 2021.3.45f1, 2022.3.51f1, 6000.0.25f1, 6000.1.0a2

Reproducible on: Windows 10 (22H2)
Not reproducible on: No other environments tested