Reproduction steps:
1. Create a new project
2. Create a GameObject (e.g. Cube)
3. Open Select Material window in the Inspector (Mesh Renderer > Materials)
4. Type in the name of the currently selected material and observe the results in Assets section
5. Remove the Material
6. Open Select Material window and type in the name of previously selected Material
7. Observe the search results Assets section

Actual result: Material cannot be found in Assets section after being removed
Expected result: Material can be found in Assets section

Reproducible with: 2021.3.56f1, 6000.0.58f1, 6000.2.6f1, 6000.3.0b3
Couldn't reproduce with: 2022.3.67f1 (Different default material)

Reproduced on: macOS Sequoia 15.4 (M4), Windows 11

Note: Section could also be renamed or new section could be added as default Material is not in Assets folder