For those interested:
Unity 2021.2 - Preferred solution
Blitting a BuiltIn Unlit Shader Graph to a RenderTexture can work with the High Definition Render Pipeline since Unity 2021.2, without any trickery. At least as far as I know, it also works with URP, HDRP and the BuiltIn pipeline, on Windows.

Then, you can just call Graphics.Blit() with a material using that Unlit Shader Graph.
e.g.
Graphics.Blit(null, targetRenderTexture, myShaderGraphMaterial, 0);
Not sure if that solution works on all platforms or with all possible render pipeline settings, please comment below if you happen to know.
I could create a repo with a working solution demo, if someone asks for it.
Previous versions (Unity 2019 - 2021.1) - Alternate solution
In previous versions, a simple (yet hackish) solution for Graphics.Blit to work with HDRP Unlit Shader Graphs can be found here: GitHub - Bers1504/unity-hdrp-shadergraph-blit: Demo of a patch to fix Graphics.Blit with HDRP Shadergraphs in Unity 2019.4
That repo contains a custom function node that can be added to an unlit HDRP Shader Graph, which works as a patch for fixing the broken HDRP ShaderGraph Blit. The problem is related to model / view matrices, which aren’t properly set up for the blit quad to correctly fill the viewport. It seems the values from the last active camera are used in the model view matrix when blitting, which is probably wrong. The camera-relative rendering setting also seems to be part of the problem, as the blit quad vertices are incorrectly changed when that feature is active in the project rendering settings.
As a workaround, the HDRP model, view and projection matrices as well as the functions to transform vertices to clip space are overridden with values that are known to work with blitting. To achieve this, a custom function patch node is added in the shader graph, and its sole purpose is to provide an injection point for overriding matrices in the final actual shader, generated from the Shader Graph (yes, that is super hacky and fragile as it assumes a certain shader code expansion order and also assumes undocumented transformation function names - use at your own risks!).
Anecdotally, without this patch, it is sometimes possible to see a tiny misplaced quad being rendered, when calling Graphics.Blit() while the last active camera happens to be at (0,0,0).
Finally, a reminder that Built-In Unlit Shader Graph are known to work in Unity 2021.2 without this ugly patch, so you should really use the first, preferred solution if you can.[/code]