I love these little things they keep sprinkling into the narrative! They give their whole relationship much more depth and dynamics, it's really sweet. You forgot one thing, though:
Their first word, apparently, was "bhai" as well 😳
Usually, your first word is mom (not always, I know) and if a child/someone gets their first salary, they give it to or buy something for their mom/wife, here tho it's different. Rudra himself said in the hospital that for him, Shivaay is his mom, his father, his everything. Yes, sometimes Shivaay has a similar role for Om but mostly, Om and Shivaay seem like friends (of course, beyond normal ones) - they understand each other so well and can share their worries with each other. Shivaay hardly opens up to anyone but we have seen that even he, when something bothers him, comes to Om to find some peace - like he did after giving Anika that check.
And Om and Rudra, we can see their dynamics very clearly- at times, Om is like his best friend and accomplice, someone whom he can approach and blame for his misdeeds, lol (then, he's "O") and other times, he is the brother whom he can seek comfort and support from like, when he's emotionally in turmoil (then O becomes "Bhaiyya"); I find that very sweet. Also, during that Bindhi scene, Rudra told Om that Om himself says he loves him more than his life.
Hope to see more layers of their relationship unravelled throughout!