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Headcanon that even though Donnie is bad with feelings/physical touch, his brothers still seek him out for comfort because he's always there for them.
Leo wants to talk with someone about the argument he just had with Raph? Well, Donnie might be a bit awkward with emotions, but he's sure a good listener. He gives very honest advice; he'll tell Leo when he needs to go apologise, but he doesn't judge Leo or pry on the situation. Donnie's very calm about everything, and Leo gets very comfy just confiding in him about things.
Raph needs to not be alone because Savage Raph is acting up? Donnie is consistently in his lab. Sure, Donnie kicks his brothers out a lot, but that's mostly when Leo drops by to annoy him. Raph doesn't annoy Donnie, he doesn't necessarily want any kind of touch or special attention. He just needs to be around someone sometimes, and Donnie is perfectly fine to provide that.
Mikey is anxious/worried about something? Donnie is great at rationalizing stuff! He can and will spend twenty minutes explaining why the things Mikey is anxious about will never happen. Plus, Donnie is... surprisingly good at managing stress? His "data collection" is basically just an easy way for him to ground himself. Donnie has little tricks for when things get Too Much, and Mikey starts to pick up on these habits/use them to make himself feel better.
At first, I think Donnie is kinda oblivious to this, but once he realizes what's happening, he starts leaning into it? Like, he starts paying more attention when Leo wants to talk with him about stuff, instead of constantly dismissing his brother. He notices that Raph will come to his lair nearing a Savage episode, so he sets aside simple tasks for Raph to distract himself and feel useful. He realizes that Mikey is imitating him, so he keeps track of which coping mechanisms Mikey finds helpful.
Just... Donnie supporting his family, in his own way.