*cracks knuckles* Okay kids, buckle up. This is a story about how two soldiers who fought on opposing sides in The War meet and learn to get along.
So, the reason I think this could work is because, like Rein, you don’t really hear Soldier denigrating any of the omnic characters pre-game. He’s not actively prejudice against omnics like Junkrat, Zarya, and Torb are. That isn’t to say that I don’t think there’d be some uneasiness there, but it’s less of an uphill battle.
So in this case, I think Bastion gets picked up by Overwatch because they understandably cause a bit of a stir when people see an old relic of the war up and wandering around and chirping at their bird friend. Neither Rein nor Soldier are part of the team that picks them up, which is for the best, but Soldier is definitely waiting on the helipad when they get back.
The first meeting is... tense. Winston has explained to Bastion what to expect, but they’re still confused, nervous, and unsure. So when they see Soldier just casually propping his rifle on one shoulder, it’s probably a bit upsetting. But the fact that Bastion can EMOTE being upset is what tips Soldier off that this... isn’t just some relic of the war. This is a being who, like Zenyatta, appears to have emotions.
They sort of circle each other for a few days. Soldier is looking for more signs that Bastion is a person (which is pretty obvious tbh, even to him), and Bastion... well, Bastion is mostly just trying to stay out of everyone’s way for the most part. But unfortunately for poor Bastion, at some point they end up in a position where they’re with Soldier and can’t easily get out.
Before Soldier triggers a panic attack (and good god, he can tell this unit has honest-to-goodness PTSD, it’s the damnedest thing), Soldier stows his rifle and his tactical visor and is very calming and soothing and is just like “all I want to do is talk.” And now that he knows that Bastion is person enough to suffer recognizable psychological damage from what they’ve been through, Soldier knows how to handle them. He’s handled plenty of other folks who’ve gone through similar, and he says as much. He talks about the ways that the people who’ve served under him previously had coped. He talks about how he, himself, has tried and failed to cope. He recommends that Bastion go take up robot meditation with Zenyatta, since it seems to have done wonders for Genji.
And Bastion is just so taken aback by this. They sort of half-heartedly agree to take Soldier’s advice, but the next day, instead of joining Zenyatta to meditate, Bastion joins Soldier for his morning PT. At first Soldier is shocked, but then he’s just sort of like “... okay...” and starts jogging around the watchpoint with Bastion trailing behind him. And that just sort of becomes a Thing. Other members of Overwatch know that if they need to find Bastion or Soldier, they’ll be running together in the mornings, rain or shine.
Sometimes, Soldier talks to Bastion, but mostly Soldier keeps to himself and so Bastion takes this as an opportunity to talk. They mostly talk about things they’ve seen or funny shit people have done because they didn’t realize Bastion was looking. They talk about Ganymede a lot. They’ve done SO MUCH RESEARCH on Ganymede with Athena’s help. (all of this is, of course, in Bastion’s trademark boops and beeps, and they realize that non-omnics don’t understand but they still feel better for having SAID the things, and Soldier does look like he’s paying attention most of the time)
But then, one day, when Bastion is discussing making sure that Ganymede has a proper diet while they’re so far away from his native habitat, Soldier stops and looks at them and is like, “Why ‘Ganymede,’ though?” and Bastion could die of embarrassment because THEY DON’T KNOW HOW LONG SOLDIER HAS BEEN ABLE TO UNDERSTAND THEM
And Soldier picks up on this and chuckles awkwardly and is like “I’ve been learning because I figured you could use some more friendly ears other than just Athena and Zenyatta.”
So that’s how that relationship starts and how they begin to learn from each other and pull each other through the bad times.