P: Horizontal flip, opens upside down after "Edit In Photoshop"

Yes, it will work correctly when using 'Edit in PS' or Export, but the OP said "Then I 'open in Photoshop'  (version 20.0.3) and it is upside down."

When changing the orientation of a file inside LR you need to perform a 'Save Metadata to File' operation (CTRL/CMD +S keys).  This allows other programs to read the EXIF orientation correction data and apply it on opening.

Not when opening from Lightroom???  I have auto write to amp turned on but believe if you open from Lightroom all Lightroom settings are honoured.

In Lightroom CC Classic v8.2 I have an image that I flipped horizontally.
Then I 'open in Photoshop'  (version 20.0.3) and it is upside down.

When changing the orientation of a file inside LR you need to perform a 'Save Metadata to File' operation (CTRL/CMD +S keys).  This allows other programs to read the EXIF orientation correction data and apply it on opening.

Try opening one of the problematic files directly with Photoshop from the HD (not through Lightroom)

No problem with .orf files (Olympus), neither .tif nor .psd
macOS 10.14.3 PS 20.0.4

I updated PS to 20.0.4 and the problem remains. Also, a vertically flipped image is rotated 180 degrees.

Source file was a CR2 raw file from Canon 70D, 350D and 400D.
It doesn't occur with a SONY ARW file (camera = A580)

I dont see this problem with a JPG or PSD (from a Canon source file) - however for these I have the dialog asking if I want to open the original or with LR edits. Maybe this dialog handles the orientation fields correctly.