Short answer: No, your ticket is not valid for the short trip between the main station and Petershausen. In many cases, it is actually possible to do something like that with a Sparpreis ticket through the City-Ticket concept but it does not apply to Super Sparpreis tickets.
From December 10, 2023, the rules are changing for discounted tickets. After that date, a city trip can be included in a Super Sparpreis ticket but you need to name the exact stop or station when booking the ticket. The same rules will also apply to Sparpreis tickets (so you're losing a bit of flexibility there).
Your best bet if you want some peace of mind in this case is simply to get a local transportation ticket for one zone for €2.80. It is also valid on RE trains as long as you stay within one single zone within the area covered by the Verkehrsverbund Hegau-Bodensee, which is the case for the Petershausen-Hauptbahnhof trip.
Rules for full fare tickets are quite different. In this case, as explained in Board German train from next station, all the stations within the city are treated as equivalent. On top of that, you are also allowed to make use of local public transit in Konstanz on the day you leave or arrive there, without having to mention it when booking the ticket.