So - after digging into using the Compositor for texture modification and then trying to expedite setups, I realized something that users are not aware of for the most part.
Textures USED to be in the Textures tab of the Properties tab, under a main heading of Textures with subheadings of Brush and Brush Mask after GSOC paint project. These textures were from Blender Render, the old renderer that was chunked awhile back. We got Cycles and then Eevee, so it made sense things would change.
So the Texture Paint Tool is being upgraded to an Asset in 4.3, and that brings paint back in the spotlight for sharing ideas. Live Compositor is also a go already in 4.2, and is really cool to work with. What’s my problem? These two areas are still using the Blender Render textures that are holdovers, and even the Displacement modifier shares this set of legacy textures and appears in the Texture Properties Panel.
Why is that a problem? Well, my good friends, Eevee and Cycles use a newer set of textures that fit in the kernel and keep things neat, and the Compositor is supposed to be working with those renderers so you would think that if you set up a dummy object with some textures you’ve worked out that you could reference them in the Compositor - but no, the Compositor is using brush textures from the texture node editor or the direct brush texture from the Texture properties panel.
Okay, work out some cool math in the Texture Node editor and then bring that to the compositor - yeah, except it is only showing if it is in the active brush texture, that tree disappears once the brush texture is changed. That editor is also holdover and not very stable.
Whether sooner or later, the Blender Render textures really need to be gotten rid of and replaced with the same set that is used in the render engines so that Blender can have a Global Texture Editor. Compositor work should be able to be gotten on quickly and not have to go looking to figure out where to get the texture from - of course, if you have opened an image texture in the Image Editor or in a Shader, that is accessible just fine in the Compositor by adding an Image node where you will see all the choices of images in the dropdown.
I know that the devs will address it eventually, but I feel like the users need to be aware of this. I am a big user of procedurals in brushes, so it might seem weird that I am saying to ditch a very useful set in favor of another, but I honestly want a Global texture solution so there is no disconnect to displacement or texturing or compositing.