I'm assuming you are using Lightroom Classic, as Photoshop is not included in the Lightroom-only plan.
It's not "automatically saved", when you have finished working on the image in Phososhop you must manually use the "Save" option (not "Save As"), then the updated photo should appear as a Tiff or PSD file (as per your Lightroom Preferences) alongside the original image in Lightroom.
If you've done that, and still not seeing the Tiff/PSD, there are a few possible reasons for that (perhaps you're using a filtered source, or maybe the selected sort order means the returning derivative is not sorted alongside the original). Right-click on the original file, select "Go to Folder in Library" and you should see the derivative Tiff/PSD alongside the original (make sure the sort order is set to Capture Time or File Name).
Did you ever get any answer for this issue. I'm having a very similar issue, and can't find anyone who can assist. There is an endless amount of info/video's out there on the internet for Lightroom Classic > Photoshop workflow, but minimal info/discussions on the Lightroom Cloud based Desktop version.
I am also looking for an answer to this issue. I've recently updated computer and any photoshop edits I make are still sitting in the Temporary Edits file within the Lightroom Library cache. I don't know how to fix it! Help!