LRClassic (LRC) and LRcloud (LRc)

Not to mention that the communication between PS and LR seems poor to me: you lose all the history of edits when coming back from PS to LR (and again if this is not the case pleaase advise on how to do it).

By @eric32035440sekv

The reason for this is technical, and would apply to any software (not just by Adobe) that works the same way:

• Lightroom and Lightroom Classic are parametric editors, so edits are applied to the original but not rendered into it, for maximum flexibility. There is no single file that exists with the edits until a copy with edits is exported. 
• Photoshop is a traditional direct pixel editor, so edits are rendered to the original file. It isn’t necessary to export for other applications to see the edits, because the original has been modified with them. 

If you send a file from Lightroom (or Lightroom Classic) to Photoshop, there is no choice but to render all Lightroom edits into a new pixel document that is handed to Photoshop. Especially for raw files, because Photoshop cannot handle raw files on its own. (Without Lightroom, any raw files you open in Photoshop must first be rendered into a Photoshop document by Adobe Camera Raw.)

When you finish in Photoshop and return to Lightroom, the old edit history isn’t there for two good reasons: It’s a new, separate file, and the edit history belongs to the original file, not this new one. But also, it would not make sense: The version sent to Photoshop is a copy with Lightroom edits rendered into it, so if you transferred the Lightroom edit history to that copy on return, the image would now have the same corrections applied twice, which would be wrong. The earlier round of corrections would have been baked into the rendered pixels on the way out to Photoshop, and a preserved edit history would apply them again. So if you had applied +1 Exposure, copying the original edit history to the rendered file returned from Photoshop would result in +2 Exposure and that is not what you expect. So it’s a one-way trip out, and if the copy comes back to Lightroom it’s a new file with a new history.

All of this goes back to understanding that Lightroom and Photoshop are two very different kinds of image editors, so they can’t simply transfer edits back and forth. You would have the same problem transferring edits between Capture One (a parametric editor like Lightroom) and the GIMP (a traditional direct pixel editor like Photoshop).

The design choices made by the Adobe teams working on Lightroom and Lightroom Classic was to NOT have one catalog in use for Lr and LrC. Only they can speak to the reasons. It is extremely rare for them to make any statements in these forums, and on those extremely rare occasions when they do make such a statement, it is never to answer WHY questions.