Templates are not immediately shown in the Shader Graph Templates Window when it's opened in Play Mode from a Visual Effect Graph's Node

Steps to reproduce:

1. Create a URP 3D Project and wait for Search indexing to complete
2. Install the Visual Effect Graph Package
3. Create any Visual Effect Graph and wait for Search indexing to complete
4. Enter Play Mode
5. Open the VFX Graph and add any of the Shader Graph Output Nodes
6. In the added Shader Graph Output Node click the "New" Button to create a New Shader Graph and set it
7. Observe the Shader Graph Templates Window
8. Add anything to the Search field

Actual results: Templates are not loaded in the Templates Browser if the Templates Window is opened in Play Mode for the first time. Entering into or editing the Search will start showing the Templates

Expected results: Templates are shown immediately

Reproducible with versions: 6000.6.0a6, 6000.6.0a7

Not reproducible with versions: 6000.6.0a5

Can't test with versions: 6000.0.76f1, 6000.3.16f1, 6000.4.9f1, 6000.5.0b10, 6000.6.0a3 (No Shader Graph Assignment from New Template feature)

Tested on (OS): Windows 11, macOS 26.4.1

Note: Might need to rebuild index on 6000.6.0a5