Is Aizawa surprised to come back to his on-campus apartment after a unscheduled patrol from a sudden villain alert only to find three children passed out together on the couch? No, no he is not. Does that keep him from pausing at the entrance to look at them? No, no it does not.
While he's looking them over from afar, making sure they're all still alive and uninjured, he takes pictures (because, despite what he tries (and fails) to portray, he's weak to cute things and can't resist). Luckily, he set up a nanny cam, so he could see all of the cuteness (when he wakes up tomorrow because he's about to faceplant into the carpet, he's so exhausted). And watch he does, after Izu and Kota leave in the morning, and Eri is picked up by 'Zashi and 'Muri, he settles into his bed with his cats and watches.
He skipped through the part where Kota is dropped off, where he gets the emergency call out, where he calls for Izuku to babysit, and starts watching at the time where he had just left.
Izuku walks in with a bag full of what he can only assume are blankets, pillows, and games. Eri looks up from their coloring books first and nearly blinds them all with her positively radiant smile. "Deku-nii!"
He dropped his bag and knelt on the floor, arms wide for a hug, smile just as bright as the girl's, "Eri-chan! Kota-kun! Hey you two!"
Eri had already thrown herself into his arms as Kota slowly stood up, customary scowl lightened when he walked over to them. Izuku snaked out an arm and, before the kid knew it, he was pressed against both Eri and Izu in a tight and comforting hug. He was stiff for less than ten seconds before he let himself melt into the hold.
Izu stood up and relocated to the couch, easily carrying the kids with him. They stayed like that for a few minutes, in silence, before Izu asked, "so, how are my two favorite kiddos in the whole world doing?"
That prompts Eri to go on a long, excitement filled explanation of what she'd done the past week (even the parts Izuku had been there for). Izu's heart melts at the beaming smile Eri gives (as does Aizawa's, though he'll never admit it) and when she finished, Kota gives his own brief overview of what he's been up to the past few months. At both the kids' insistence, Izu tells them the bare bones of what he's been up to and they go back to coloring after that, neither willing to move very far from the green haired boy.
Aizawa watches the full two hours of them coloring and complimenting each others' works. Once Eri is visibly tired, Izuku pulls out two of the fluffiest, softest blankets and wraps one around each of the kids' shoulders. Soon enough, the soft warmth is lulling them both to sleep, but not before Eri and Kota team up to bully Izu onto the couch so they could sleep next to him. Then there's another two hours of them sleeping, barely moving except when Eri accidentally slaps Kota's face when she flipped to her side.
Whether or not he watched it multiple times is up for debate, and he'll take that secret to his grave (it was five times, Nezu sent pictures of his Soft™ dad face to the staff's group chat). And if there's a warm clinching feeling in his chest when he watches it, well no one's there to call him out on it (not that anyone would, Eri makes everyone soft, add in Izuku and you're guaranteed to melt).