A lot of people here use Airalo for eSIMs, and I have used them in the past and been very happy with them. However, I have switched to a pay-as-you-go eSIM called Bcengi. Instead of the typical eSIMs, where you buy fixed data bundles for specific areas that expire, Bcengi is a pay-as-you-go eSIM. You load a cash balance of $10 or more into your account (I put in $25) and pay only for the exact amount of data you use. The network adjusts rates and connects automatically as you cross borders into different countries. When you get home, you can turn it off, and then turn it back on again the next time you travel outside the country.
So there's no need to buy separate eSIMs for different countries or areas, and you don't lose any leftover data at the end of it. It worked really well for me. I used it in Norway after my T-Mobile slowed down for about ten days and spent $6.88. I used a credit card to pay the $25, which automatically reloads when your deposit is down to $10. And you can stop the automatic reload at any time.
The biggest advantage to that is that you don't have to limit your eSIMs to specific countries like you would if you bought an Airalo eSIM or one of the other eSIMs offered out there. However, if you don't travel a whole lot, it may not be worth it for you. In that case, you would look for an eSIM that covers Italy, Austria, and Germany. Most of them have a Europe packet, so it would cover those three countries for the time period you want.
So if you go that route, I would go ahead and purchase the eSIM before you leave the country, but you don't activate it until you're ready to use it. Once you activate it, that's when you start paying for it, so you can wait until you burn through your Verizon plan data. This helpful site on the Airalo website might give you a better idea of how it works. Free to come back with questions. https://www.airalo.com/how-airalo-works