This scene was what always confirmed to me that Ozai cared about Ursa. He obviously couldn’t tell Zuko why she had gone - it would amount to telling him that he had gotten the throne through treason, and children are hardly the best secret-keepers. So he keeps silent, sacrificing the chance for Zuko to get closure for the sake of maintaining the lie Ursa helped him craft.
Yet he lingers contemplatively by the spot she had recently occupied and stares at the fountain that won’t play anymore. That doesn’t scream ‘heartless husband who’s having a blast now that his annoying wife who could poison him is gone’. I wouldn’t even pin it on relief, which he’d probably be feeling in the comics’ version after eliminating a serious threat to himself. The whole mood here points to Ozai being contemplative about her departure.
It could be that he loved her deeply and was mourning the loss. Or maybe he hadn’t even realized that he cared for Ursa up until this moment, when he realized she’d never sit in that spot again.
Wherever their relations fall on the Urzai spectrum, his mood here is clearly one of gravity. He wasn’t unaffected by Ursa’s departure. What more, Zuko is able to intuit that something’s wrong without Ozai having to say a single word.
This is an interesting moment of communication between Ozai and Zuko. In normal situations, Zuko is probably used to Ozai always having something to retort with - especially if it’s talking to him. Really, it wouldn’t have been out-of-character for the confrontation to have taken place somewhere in the palace, with Ozai looking all regal as the new Fire Lord and curtly telling Zuko that Ursa’s whereabouts were none of his concern.
But Ozai’s out by the fountain, and he says absolutely nothing. This isn’t typical Ozai, and Zuko knows it. Whatever emotion Ozai is displaying (we can’t see his face, but presumably Zuko can), Zuko knows that only something serious can make his father react this way. So whatever happened to Ursa can’t have been good.
It’s also interesting how Ozai takes Ursa’s place by the fountain at the same time as he figuratively takes her place as Zuko and Azula’s chief caretaker. This is illustrated nicely by how Zuko is the one to rush out towards the fountain, where Ursa was often seen, and find his father there instead. Where a mother once was now stands a father, and Zuko’s not sure if he’s happy about it.
That’s why I also see this moment as the moment where Ozai resolves to take the reins and assume sole responsibility for Zuko and Azula. Just like they would have to accept without explanation that their mother was gone, they would have to accept the new life Ursa’s sacrifice had given them.
In light of this, I like to think that Ozai did place an importance on being a parent towards his children. But he also wanted to make sure they were raised his way from now on - the way a Fire Lord’s children should be raised. He wasn’t just dragging them along like unwanted luggage, or even plotting to use them as tools. Not yet, at least. In the wake of Ursa’s absence, he stepped up to the task with awareness and determination: he wouldn’t be soft like she was, but he would mold Zuko and Azula to something befit of the title ‘prince’ and ‘princess’.
Unfortunately, these good intentions paved the road to hell.
