The old door frame has been removed. Does the door jamb need to be renewed?

First measure the inside dimensions of the door opening and let us know. Does a modern door frame with DIN dimensions even fit in there? How large is the frame overlap, i.e., the side overlap? The old door frame was plastered in. To me, it almost looks like from the GDR. Western doors don’t fit into GDR door openings. They were smaller; you have to enlarge the door dimensions. It might be that you first need to plaster the sides a bit so that the new frame fits and also aligns flush with the wall. I wouldn’t just use construction foam for that. But send the measurements first.

If you don't want to cut anything, then the frame must have a higher covering dimension

If you don't want to trim anything, then the frame must have a larger casing dimension. There are also different possibilities for that. That means the trim on the outside must be wide enough to cover the old rebate of the previous frame. Otherwise, trimming is necessary. Otherwise, the opening fits your project without any problems.

That quickly looks ridiculous