When Alina asks if there is any mail for her, the man glances down at the stack of mail but never thumbs through it. He then responds that she doesn't have any mail. If you look closely, he does do a brief sift through the mail. The gesture happens to be obscured behind Alina in the way the shot is framed, but his body language and the sound effect of rustling paper combine to convey the action is there.
The archivist's glowing fingerprints on the drawer with the Little Palace blueprint is crucial to Inej locating it quickly, but in the preceding scene of Kaz's visit, the archivist's fingers don't make contact with anything of his or that he has touched.