My initial response is no. I'd stay on the airside, go through passport control, locate my departure gate for Rome, find a place to ease out and have breakfast.
There are too many variables to consider, especially when you are arriving jet-lagged to a place you know nothing about.
Keep in mind that you will have to go through passport control and find your way to your departure gate in time to be there at the time your airline wants. The plane could be late. Passport control could take longer than you might imagine, especially if several planes arrive at about the same time. So could locating your departure gate.
And you don’t say when you are going. If it's soon, according to the links I've posted below, Covid protocols could slow things down considerably. See especially the link and info on transferring below.
Full disclosure: Schiphol is my favorite European airport. It's where I arrive and depart from whenever I can. But I've never had a layover there. I've used Amsterdam as my starting and ending place for those trips.
This is a link to the Schiphol website in English.
This is a link to the section on transfers. This is from that section:
Do I need to take another test when transferring? No, that is not necessary. If you stay at Schiphol during your transfer, you do not need a new negative COVID-19 test result. The test result you had upon arrival at Schiphol remains valid during your transfer, including any potential delays. If you leave Schiphol during your transfer, this counts as a new journey and you are required to present a new negative test result. You can find out more on the Dutch government website.
This is a link to an interactive map of the airport as well as to pdfs of different parts of it. Places to eat are shown. They are identified as before and after security on the interactive map. If you stay airside, you will be after security and you can even find places near your gate.