Lightroom Classic 13 not compatible with Photoshop 2024, various plugins

Lightroom Classic 13 and Mac OS Sonoma do not seem to get together too well. Whilst in LRC 12 I had aboslutely no problem with Sonoma, I can report the following issues with LRC13.

1. In the Develop Module I use the cursor to move between images in the filmstrip. While the images do get moved, the preview in the main window stays the same. 

2. I export a photo for further development in Photoshop 2024. I do the edits and then hit "Save." The photo does get saved, but not next to the original one (as it should do). It gets saved... at the top of the directory ebcause somewhere in the process its "Capture time" got changed to today's date! I do not know whether LRC or PS is to blame, but these are serious issues that Adobe should not have allowed in the first place.

Does anyoone have any idea how to fix them?

I have uninstalled and reinstalled both the Adobe and Sonoma, I have run catalog optimnsiation, I created a new catalog and imported all my stuff from the old catalog, I spent hours with an Adobe agent on the chatline - nothing seems to work and no one seems willing to even acknowledge the glitches.

If anyone knows what to do, please help.