Have latest releases of LR and PS, Windows 10 Pro. A JPG file in LR, Edit In Photoshop as a Copy. In PS add layers. Save As PSD. Back in LR, file shows up as "-Edited" but it is still a JPG, and none of the layers adjustment has been applied.
This is expected. Yopu should choose Edit with Lightroom adjustments. If you choose edit a copy, Lightroom makes a copy of the original, appends -Edited to the name and opens that in Photoshop. So you will end up with a jpeg file after everything except when you choose save as from Photoshop and save the file as a tiff or psd. If you choose Lightroom adjustments, Photoshop uses camera raw to open the file and is instructed to eventually save the file as a tiff or psd depending on the preference you set in Lightroom Classic.
In the dialog that comes up try using the "Edit a Copy WITH LrC adjustments". That should then create a PSD ot TIF, dependking on the setting you have chosen in the external edting section of the LrC Preferences.
Using just the Copy or Original options and usiong Save As may not.