Deutsche Bahn – Suddenly it is announced that my train will not reach my destination, my Sparrprise ticket is valid

The railways in Germany are very good at offering alternative means of transport if the train you are planning for some reason can not be used.
First, ask all people in your area to explain if they can. Then look for a person in uniform. And if not nearby, go to the ticket office in the train station where you are.

The uniformed staff or the ticket counter staff will tell you which train you can best use and sometimes give you an alternative route.
The alternative route may not give you a reserved seat as this can not always be arranged. In first grade you can almost always find a seat or ask the train crew to help you with the search.

I have had the same problems several times in Germany, I was always there on the same day, albeit a little later than planned. And without additional costs.
If you miss your last train of the day because of your delay, they should help you reach your final destination that same night, or stop you for one night, but you'll have to ask uniformed staff or ticket office at once to have a reasonable expectation of it that they can arrange things.