DB changed my train - do I need to rebook or do I have a ticket on the replacement train?

First of all repeat after me: "There is no such thing as a train ticket".

You may believe you bought a ticket for EC 83, but what you really bought is a ticket for the route from Salzburg to Bolzano, and a reservation on EC 83.
That ticket may, or may not be a discounted ticket that carries the restriction that you take the booked train, but once that train is removed from the timetable that restriction is lifted. So your ticket is basically good for any train on the route, and you are free to pick one from the schedule and just travel on it. In fact, that is what you are expected to do.
You may have noticed that train tickets often come with the mention that you should check the schedule closer to the departure date, and adjust your travel if needed. In the past we even bought train tickets without even knowing the schedule, as prior to the internet figuring out what the schedule of a local train in Austria would be while in a ticket office in Belgium was often not possible.

Now as to my reading of this: OBB is responsible for the trainset on that route (even though you can buy tickets from DB), and they are gradually replacing the old EC consists with newer RJ consists. These trains are different enough that they cannot just move your reservation to the new train. So you will need to exchange your reservation, which you should be able to do at the station. Any major station, not just in Salzburg. Or you can ask for a refund on the DB site for your reservation only (can even be done afterwards), and get a new reservation on DB or OBB. Both sites have a "reservation only" option, but on DB it is a bit hidden...

It wasn't DB that changed your train, but ÖBB, which operates this train. They are in the process of replacing the old EC sets with the modern RailJet, but DB has no way of knowing when the individual trains will be replaced. The replacement is definitely to your advantage, as the old EC sets were already a bit run down (they should have been replaced two years ago, but delivery dates are always a matter of luck in the European rail industry). You need a new seat reservation (it's cheaper with ÖBB), and for the old one you should request a refund - if you are in Munich beforehand, directly at the station, otherwise on the DB website.

@sla019 the first train operator is Österreichische Bundesbahnen but the 2nd train, the one that was changed, is operated by DB Fernverkehr AG (according to the journey on the DB website). But thanks for the tip about changing the seat reservation Munich since I will be in town earlier in my trip.

And @WengenK thanks for the detailed reply.

OK, I should have been a bit more precise: There is a difference between the operator and the railroad that provides the rolling stock. In the case of an EC from Munich to Italy, the operator is of course DB within Germany and ÖBB in Austria and so on. But the train itself is provided by ÖBB. You can see this in the train classification: RJ (RailJet) is a designation for the fastest train of ÖBB, the equivalent of the ICE of DB. And DB has no influence whatsoever on the choice of rolling stock. European train travel can still be a little, well, let's say entertaining. Have a good journey.