I have an idea that Shadow doesn't actually know Tails' age.
Like no one ever told him and he just assumed that he was only slightly younger than the rest of them, by like maybe a year or two. But him thinking Tails close enough in age to everyone that he never felt the need to get a concrete age on Tails. Shadow mainly drawing this conclusion because of how smart Tails is, the fact they bring him everywhere, and that Eggman even has admitted to have been fighting Sonic AND Tails for years now. (He thought Tails was just short for his age).
Later though this comes back to bit him in the ass.
For what ever reason Tails and Shadow have to team up on a mission just the two of them and right when he's about to leave to meet Tails, Rouge drops just a little unthinking comment of
"You better keep an eye on that little 8 year old genius. He's smart ~buuuuut~ he was raised by Sonic."
And that makes Shadow full stop pause because
".....I'm sorry....what do you mean he's 8????"
And thus Rouge has an absolute delightful bit of news to drop on their resident angsty hedgehog and enjoys watching him go full 404 error mode over it.
Shadow meanwhile is rethinking every single interaction he's ever had with Sonic and Tails. MAINLY all the times he's attacked Tails (mostly kicking the back of his head). Because now he has the context of he was straight up attacking a literal child that hadn't even hit the double digits yet.
So now Shadow has to have all this circling his brain while also on a mission with said child and tasked with keeping him safe (as threatened by Sonic who had to go on a separate mission from them).
And he's just there watching as this 8 year old not only hacks circles around Eggman's firewalls but also dismantling his robots as he fights them and holds his own fairly well the whole time.
And like Shadow is impressed but also still in little bit of the mindset of "OMG THAT'S A BABY!!!!!"
It all comes to a head when Shadow keeps hovering around Tails and Tails is getting a little annoyed/stressed about it because Shadow has barely let Tails go two feet without being RIGHT THERE with his usual resting bitch face and not saying anything. So Tails snaps a little bit asking if Shadow has a problem with him or what he's doing since he's hovering and Shadow just replies with
Which was not what Tails was expecting to be asked so he just confirms and Shadow just goes quiet and gets a far off look on his face.
After that though he does start actually talking with Tails and they both end up having a good time hanging out on the mission together and find they get along well. Shadow secretly can't wait to bring his bike and guns to Tails for him to modify with what modifications him and Tails started to basically geek out over (not that Shadow would ever admit it).
The mission goes fine and they're meeting back up with everyone but then for some reason when Shadow sees Sonic it's ON SITE. Just attacks him and they speed off in the now random fight while everyone is asking Tails if something happened to which Tails has no answer for them.
Shadow meanwhile start just laying into to Sonic about how stupid and irresponsible he is to let such a young kid go with Sonic and everyone on such dangerous missions/adventures.
Sonic finally getting an idea at least why Shadow decided to start a fight. Keeps retorting with how he'd be a hypocrite not letting Tails be free to do what he wants when he's been fighting from a young age too, etc, etc.
It goes on for a bit with insults, ideals, and hits thrown back and forth before they both finally calm down and in the quiet after fight Sonic goes into the story of how he meet Tails and WHY he had to bring him everywhere with him since neither had a place to go (and the one time he tried to find Tails a permanent home it was a trap from Eggman). And how their only home turned into wherever the other was.
Which almost makes Shadow want to hit Sonic again because that means Tails was even younger than he is now when he started to fight Eggman. He doesn't but it's a close thing.
After the fact Shadow has a whole new little bit of respect for Sonic but he mainly has a lot of respect and almost awe for Tails and his capabilities at such a young age.
And if he now checks on Tails and brings him things to modify to the point he starts to actually bond and form a friendship with Tails...that's no one else's business.
(p.s. this is not shipping them, I see Shadow as another older brother for Tails so please to tag as shipping them)