Unfortunately, there is no easy way to find out the direction of travel and seating on the DB website. However, there are some meta-pages that make this possible with some effort. The easiest to use is fernbahn.de.
note your train number from the DB app
go to https://www.grahnert.de/fernbahn/reihung/reih0043.html. In the upper right corner, set the language to English.
search for your train number, let's say ICE 622, departing Munich 14:47.
the route of the train will be indicated as follows: <= Munich-Frankfurt / Frankfurt- Dortmund => , i.e. the train changes direction in Frankfurt
So for your leg to Nuremberg applies: left = front. Now click on a carriage number, say 38. The seating map pops up with seat symbols where you can recognize the backrest. This means that in this carriage you will travel backwards in all seats with the numbers from 11 to 55, forwards in all seats from 56 to 85, etc.
now you can select one of the seats in the DB app
But ... What you see is the scheduled carriage sequence. It's not uncommon for trains to deviate from this for technical reasons (it's a popular DB game to keep its customers happy: announcing two minutes before departure that "the train is running with the reverse carriage order today").
So I wouldn't worry about the whole thing. With three ICE trains per hour between 14:00 and 15:00, it is unlikely that even one of the 1st class coaches will be full (the forecast for all three trains on March 19 is "low occupancy"). So just get on and occupy a free seat in the direction of travel.