Well Hannibal had probably at least 1 Syrian elephant, the rest of his elephants were probably north African, but it's also possible that it were bush elephants or Syrian elephants but the latter two are very unlikely.
Regarding the Ptolemaic empire, they probably used bush elephants
The Seleucids used mainly Indian elephants, which the seleucids recieved from the Mauryan King Ashoka between 305 BC and 301 BC, however it might have been possible that the Seleucids also deployed several Syrian elephants (if this was true they were only very small in number).
I personally think we should make all types of elephants available to each elephant faction as aor troops (Indian, Syrian, north African and bush elephants) ;I wouldn't give the Romans access to Syrian elephants since those were extinct by the time the Romans reached Syria; we could however represent them as expensive mercenaries that don't replenish.