Should a young man marry a girl with whom he committed the sin of anal sex—while she is still a virgin—to cover for her, especially after things became easy following the Istikharah prayer and the father's approval, or should he not marry her due to his feeling of discomfort towards her despite their repentance?

The sin you committed with the girl is a grave one, but no matter how great the sin, Allah's forgiveness is wider, and He accepts repentance. It is not a condition for repentance to marry the girl with whom you committed the immoral act. Rather, repentance is achieved by abandoning the sin, feeling remorse, and resolving not to return to it, while concealing your own misdeed.

If you do not feel acceptance in yourself for that girl, then it is better to not marry her and to seek someone else. As for Istikhara (prayer for guidance), the preponderant opinion is that a person should proceed with the matter for which they prayed Istikhara and not abandon it unless Allah diverts them from it.