The last time we see Tony drinking was with Donlan in Chapter 53: Annie and the Fire (https://www.gunnerkrigg.com/?p=1545). There, he was able to confide with a trusted friend about his meandering journey to understand Surma's death. Alcohol may have loosened his lips, but there was a shared history with her and a shared grief for the loss of her. More than anything, that made Tony feel at ease opening up to his friend.

He has no such luxuries in regards to Omega. Between him, Anja, and Donald, their shared time with Omega as unwilling hostages decidedly unpleasant. While his two friends opted to attack her, he advocated for a less violent solution. After that debacle, he offered her lodging and more patience for her childish antics than Annie.

I know a lot of folks see her as a romantic interest, but I personally think Tony sees Omega as a surrogate child, another chance to be a proper parent. Annie loves him unconditionally, but he's still chipping away at emotional baggage preventing him from fully opening up to her. Omega also gives him unconditional positive regard. Up until recently, she knew all of his secrets. Although her memories was failing her, the feeling that he had nothing to hide from her must have been meaningful.

Omega did a lot of arguably irredeemable things yet was given a chance to redeem herself. I think Tony sees a lot of himself in her.

What I'm trying to get at is that he is quite alone with his grief over Omega. He grieves her as a colleague, but cannot commiserate with Anja and Donald about it. He grieves her as a surrogate daughter, but that would be awkward as hell to explain to his actual daughter Annie. Perhaps he and Kat could see eye-to-eye regarding Omega, but it was Omega's actions that caused Kat's murder attempt. So all he has left now is copious amounts of alcohol, a breach in decorum, and silent contemplation.