There is no information of any sorts as to session tracks over and above what's been released.
There's also no indication whether the 'Dog' recordings were unique or part of Chiccarelli's asserted wealth of material stemming from the La Fabrique / Forum Studios creative period (remembering that Dog was recorded in 2018 very close to LIHS).
Yes, Dodwell did gleam:
"Can I ask what's next for you, Morrissey? I know you have some tour dates coming up soon but do you have any long terms plans for another solo album or project - or haven't you thought that far ahead just yet?
We have recorded a new studio album, but when it's released depends upon how much breathing space is allowed California Son. So, anything could happen... and anything usually does happen. It's an album of 12 original songs, so is, in its way, the follow-up to Low In High School. We recorded it in France once again, and it's fantastic. I would imagine a January release, but I don't mind if it's later."
Looking at the running time, it would seem an extra 12th track could fit on the CD. Obviously vinyl has different considerations, but that could have worked too - so who knows!?
Regards,
FWD.