My 80 year old mother can't hear the TV without it blasting out the
neighbours. I have some wireless headphones which I can give her but the
headphone jack on the front of the set cuts out the speakers when
headphones are plugged in.

The adjacent phono plugs appear to be for game input, but I'm not sure
about the mini-din plug between the two. Anyone please know if this can
give audio out?

Alas, she can't find the manual and the Sony websites don't list that
model now in their user manual database.