maybe almost nothing at all
These what if stories are pretty much based on an overly mechanical view of history. It is more realistic to use the swimming pool view. Take out of bucket of water, put in a bucket. It doesn't really make all that much difference. Maybe you get some splashing, but...
To consider some of the events suggested...
" * The Babylonians eliminated Judah. (597 BC Nebuchadnezzar executes Jehoiachin and a large number of Judah’s population following a revolt. Later, Zedekiah, placed on the throne by Nebuchadnezzar, also revolts. 586 BC Soloman’s Temple razed and large numbers of Jews executed. "
The area is now occupied by the Samartians, and this tiny despised sect they call jews. Bablyon is destroyed by the Persians who treat the locals well, but are displaced by the Greeks, whose attempts to impose Greek culture cause a successful revolt, tho the samartian state is eventually taken over by other states. Some time shortly after 1 AD [CE is a silly term, a foolish attempt to hide what can't be hidden.], this hick lay preacher comes to the holy capitol and makes a pest of himself, causing his execution. His followers refuse to accept his death and insist he is still alive, and start preaching all over the place....
"* The Romans fought to a stalemate with Carthage during the Second Punic War. "
The 3rd Punic war follows and is a complete Roman success, ending with the destruction of Carthage [which is later refounded..]
"Currently, the Carthaginian Empire [600 AD]"
The number of states that have lasted 800+ years is zero. Each suffered massive revolution, conquest, and/or other replacement during such a period. We can safely say the Carthaginian Empire simply would not have lasted that long.
One possibility, the invasions that took out the Roman Empire also overran north Africa, so we can again suggest a revision to the actual European history.
"* Rome never conquered Greece. (197 BC-Philip V defeats Titus Quinctius Flaminius at the Battle of Cynoscephalae in Thessaly.)"
Once again, there is no reason to assume this was anything close to a final try. A generation later, another war, and Greece becomes Roman anyway.
History doesn't have any actual "what if" moments.