Issues with Sidecar and Apple Pencil

I had the same problem and solved it this way:

-I observed that the cursor was about 1cm lower on the iPad, this was due to black bars on top and bottom of the iPad screen

-In Preferences/Displays I deselected "show touchbar" and the problem disappeared (please note that I am on a german macOS so it could be named differently in an english version)

-Apple should translate the coordinates of the mouse correctly even if I display the touchbar...

I resolved the problem, using free software (from App Store) setting up screen resolutions. Apparently, iPad was set ups by my Mac with an identical screen resolution as native Mac resolution (1x, not 2x, as in retina resolutions). After I set up a retina resolution for iPad, all started working well. Also, after I did it, the resolution identical to Mac native resolution disappeared from resolutions available for iPad. At the same time the problem discussed here was resolved:

Adjust iPad screen size when using sidecar - Apple Community

The app that did it was EasyRes, but I suppose the apps discussed here (paid) would work, too

Sidecar Resolution Issue - ipad resolutio… - Apple Community

In my case (MB Pro 2019, iPad 3 Air rd gen.) running latest Apple systems, the pencil is misaligned, precisely as described any other users writing in this and other threads, whenever I use it in the mode "extend the screen". In Mirror mode, it works well. It does not matter whether I turn the Touchbar on or off. The pencil's posiotion is read relative to the entire iPad screen, as off there were no two black areas on the top and bottom of iPad screen. Changing settings, resetting Mac's PRAM does not help.

I can't reproduce the problem. Tested with Photoshop Elements 2022 & Pixelmator Pro. Perhaps there's an issue with Photoshop. Make sure it's up to date.