It’s a Panasonic kx-tgd320nz
Plugged into a splitter as the old one was
Is the phone perhaps inserting a prefix before dialling?
Take a look through the manual and look for something like "insert area code" or "insert prefix". I would guess it's sticking an extra 0 in.
Did your old phone work in the same plug? If people can't call in the issue is unlikely to be anything to do with the phone.