Squaring "my father was a diplomat" with what we see of Richard Bashir later... what if that was before the augmentations? Because nothing said there is inconsistent with Julian not really understanding what was going on; it is perhaps strengthened by it.
So assume two things here: that Julian's memory is a bit blurry and that the act of getting Julian augmented did something to Richard.
Richard is lower-level in the diplomatic service, abrasive but not incompetent. Not going to rise to the highest heights but reasonably good at his job--and very arrogant with it, because he's not yet a chronic screw-up but he's still Richard Bashir.
And then he has a son who is developmentally delayed.
This eats at him. Because he is very arrogant with it, very convinced he has a bright future ahead of him, he's a genius selflessly serving the Federation, and now here is what he would see as this secret sign of his own weakness, that someone as bright and skilled as him doesn't have a child who is equally brilliant.
So he takes his son to Adigeon Prime, and only afterwards does he realize that he now can't return to his post with the diplomatic service because it will be obvious something happened. As much as he tried to keep little Jules out of sight, he's working in the diplomatic service and traveling all over the Federation with his family. People know about Jules. People will know if Richard comes back with a suddenly genius child.
Which means the Bashirs have to completely cut ties with their old life, and since Richard was a diplomat traveling all over the Federation, that leaves a lot of skilled work unavailable to him because someone might recognize him or notice, and in any case he can't exactly use his previous work history to obtain a job. Which leaves him primarily performing low-skill jobs which are far below his abilities, and slowly growing to resent Julian as responsible for the dramatic reversal in the family fortunes. He doesn't stick to any project for long because none of it is the work he was so good at and loved doing and none of it will ever be that work; he can't rise to any position where he might gain wider recognition because someone will notice and questions will be asked, and he does really badly at a lot of the low-skilled work he can get because he thinks of it as beneath him and he hates that this is what he's been forced to when he was a diplomat. So he does it poorly, he loses his temper a lot, he's harsh on Julian, and he's getting ever more bitter as the years pass, which does nothing to improve his parenting.
Julian, meanwhile, doesn't have terribly clear memories from the time before all this was true, so he only knows that his father was a diplomat and then wasn't, and assumes that his father's chronic screw-up-ness is why Richard isn't still a diplomat. He assumes Richard orchestrated the whole genetic engineering in an attempt to make up for his own shortcomings and pushes so hard in an attempt to at least have a child who can achieve greatness, so Richard can take responsibility for that greatness by proxy when he can't achieve it himself. And in a way this isn't wrong--but it's so much more than just wanting to have a child to brag about. As far as Richard is concerned, Julian being a genius is the thing Richard sacrificed his life for, which means it had better be worth it.
Deep down, Richard knows that.
But he would never, ever admit it.
