What to Bring/leave home for 1.5 year old?

Any grocery store will have those items
There are babies in Italy

Haha I know there are babies in Italy! I'm just wondering how similar the items are to here in the US?

I would take the "risk" and check luggage. I know light packers can work wonders, but having to schlep all you need for four humans (two rolling bags, plus the stroller, plus your personal items) while also handling those little humans on the plane seems miserable.
But yes, all of that will be available. You may want to stop at a larger grocery store before going to CT.

Look up photos to get an idea. Google Venice Italy grocery baby food, and you will see that they have diapers, etc. Probably the only one listed that may be different is fruit/veggie pouches. I would expect glass jar options and fresh fruit to cut up.

For the locations you will be, the grocery stores will be much smaller, so you may want to specifically drive to a larger store at the beginning of your trip.

One of the very coolest things about traveling to Japan when my daughter was about a year old was experiencing the differences in how children are treated/accepted in other regions. In the US kids are often seen as nuisances or generally not accommodated. In Japan at least every single place we ate brought out a small bowl and spoon and often rice cracker snacks for her. It was so easy to find snacks and wipes, etc.

So I don't know anything practical about bringing a toddler to Italy, but given it's familial and inclusive nature I'd guess you're going to have no problem finding what you need. OR finding someone to help you find what you need :). Specific things like fruit/veg pouches might not be available, but there will be alternates. And unless your child has specific food allergies or concerns, that's all part of the fun!

Also, except for the very small hill-top towns we were in last year, there was a market of some sort in every town we stayed in where we bought lunch supplies. I'm guessing that will be the same where you are -- you'll be able to get bread and cheese and some fruit :)

Most grocery chains now have websites (due to the pandemic, I assume) so you can browse through to get an idea of what kid products are available. Sorry, I can't help with chains in Italy but maybe someone else can suggest names.

One big grocery chain in Italy is Conad - here’s their baby section. Looks all organic and stuff.
https://www.conad.it/prodotti-e-marchi/baby

and bringing a stroller (I know we may not use very much).

When the trip is over, would like to hear how this worked out.

I suspect if one were to make a list of places in Italy that are stroller friendly, CT and Venice finish closer to the bottom than the top

I've spent a lot of time in Italy with small children, including babies.

Don't worry about the things you asked about -- the quality and abundance of diapers, etc is just like in the US.

You didn't ask, but I strongly advise against bringing a stroller -- there are many reasons why they are a liability in Italy, including numerous hills, stairs, crowds, public transport, cobblestones, scooters, impossibly tight parking to walk through, narrow sidewalks, etc. Instead, I'd recommend a baby backpack. It's more of a strain on your back, sure, but waaaaay more flexible and useful in Italy.

Over all, our babies were welcomed and treated extremely well in Italy, by people of all ages. They were even given small gifts (bread, cheese, candy, small toys) by complete strangers. It's can be a fun place to travel with a baby -- enjoy!

I would take a stroller and a carrier. It’s really hard work to carry an 1.5yr old around all the time. A combination will work best.

If you need to check a bag then do. Babies aren’t very good at keeping their clothes clean and often prefer their own sleeping bags or blankets. You’ll need a lot of baby supplies just to survive the flight (food, milk, diapers, spare clothes, toys etc) so trying to also manage all your luggage as well could be a bit tricky.

You can buy anything you need but things will taste different so if you have a fussy baby prepare for them to live on fries and ice cream!

Yes you can find everything! Even fruit pouches, I don't know why everyone says you won't find them. There are available even in small grocery stores.
There is also a very common cookie brand for babies, and it's Plasmon, they'll dissolve in their mouths.
Don't worry, you can find everything!
Regarding the stroker, it won't be practical maybe for Venice and Cinque Terre , but if you're going to other places, it's very useful, also because you can put other things there, like shopping bags, coats etc