I can't really say if Italy will qualify in this group but having Ukraine trying their best to qualify I feel Italy should have been making preparation for getting the 2nd or 1st position in that group.
It would be a shame if Italy miss out on this tournament, because they look more competitive to give other nations problem like a challenge for the title but since England are topping the group they (Italy) need to struggle for that 2nd position to grant them qualification. As it stands Ukraine are not ready to leave that 2nd position for anything.
Chance for Italy is still good because they only played 3 matches. With those matches, they have 4 points, that are 3 points less than Ukraine that already played 4 matches. If Italy play their fourth match, they will have same total points as Ukraine. If Italy win two more matches to reach a same total matches of England, they are only 3 points less than England.
However I am realistic that Italy target should be a second position and they must solve Ukraine first. When they finish it, they can start to think of a first position.
https://www.uefa.com/european-qualifiers/standings/It has now become clear that Italy is racing for second place in the group because England is the leader with 13 points with 4 wins and 1 draw in 5 matches. Italy is competing with Ukraine. I think Italy will take the second place in the group and will be able to make it to Euro 2024. Being in the same group as England was already putting the group on a difficult level. If Italy doesn't make it past the group stage, it will surprise everyone.
I am thinking more about a second position for Italy because they will hardly to beat England in their second leg match. So it is more possible for them to claim a second position in this group as they can beat Ukraine in direct matches. They don't have big gap on the table too as said if Italy win one more match, they will have same total points as Ukraine.