Interrail to Italy

In Basel you will need 5 min max. In Lugano 3 minutes.

But do not worry. In Switzerland trains run on a strickt clock face schedule, with trains running every hour or every half hour. So there is always going to a next train if you miss a connection.

The principle of the clock face schedule, with timed short connections is actually something the Swiss copied from the Dutch

Just fly it is quicker and cheaper. There are 12 direct flights a day that take 1 hour 45 minutes compared to 12 hours and 30 minutes.by train
If one train is late causing you to miss a connection, you will waste a whole day on the train.
Also you might by lulled asleep but you need to stay awake so you can keep an eye on any bag you might have as people get off the train at each stop.

The trains operated by SBB I trust to be on time but not the others before that.

The Utrecht to Basel is a German ICE train and they have been notoriously late in the Rhine valley region. If that is the case, you will need to detour to Zurich and get a train to Lugano, then Milan.

Are you trying to avoid seat reservation fees? There are direct EC trains from both Basel and Milan, but they do require seat reservations, at least for the Italian section.

To get to Italy however taking any train to Lugan and switching to the RE there is often as fast as the EC, as between Lugano and Milano the RE trains are actually faster than the EC trains. (Because Trenitalia is still learning how to do proper interval scheduling...)

This is going to be a long, but interesting ride, as you currently still go over the old Gotthard route. Do not worry to much about missing a train, as even a delay of 2 hours in Germany will not prevent you from reaching Milan on the same day.