Shader Graph with HDRP and Universal Active Targets is not SRP Batcher compatible when the Graphics SRP setting is using HDRP asset and Rendering is using URP asset

How to reproduce:
1. Open the “SRPTests.zip” project
2. Open the “SampleScene”
3. Select the “HDRP” Quality level setting
4. Open (by double-clicking) and Save both “MOA_SG_Tint” and “MOA_SG_Triplanar_Foundation” Shader Graph assets
5. Select the “High Fidelity” Quality level setting (this is using URP)
6. Save one of the Shader Graph assets and observe them in the Inspector window
7. Repeat step 6 with the other Shader Graph asset

Expected results: Both Shader Graphs are SRP Batcher compatible
Actual results: Only the most recently saved Shader Graph is SRP Batcher compatible

Reproducible with: 2022.3.18f1, 2023.2.8f1, 2023.3.0a7, 2023.3.0b5
Not reproducible with: 2021.3.34f1, 2023.3.0a6

Reproducible on: Windows 11, macOS 14.2.1 (by reporter)
Not reproducible on: no other environment tested

Notes:

• Reproduction is very inconsistent (sometimes it takes a couple of tries switching to HDRP quality and saving shader graph assets, to have this bug happen)
• This appears to be a new instance of this issue:
  https://issuetracker.unity3d.com/issues/srp-batcher-on-the-shader-graph-with-hdrp-and-universal-targets-is-not-compatible-when-hdrp-package-was-installed-after-urp
• Whichever Shader Graph was last saved becomes the only one "compatible" until another one is saved