Do we ever see Ozai actually care about stopping Aang?
Honestly, other than Zuko, does he ever send out ANYONE to find the Avatar??
Zhao stumbles across him and kinda sorta adds 'get the Avatar' to his 'to do' list, as like a potential hobby he can pick up during his actual job of harassing Zuko and killing the moon. The siege of the North is a much bigger deal to him, and it seems that Aang being there is a convenient happenstance, not the main reason for the invasion.
Then, Azula is sent to capture Zuko and Iroh, runs into Aang and decides to switch targets. She is never told to go after him by the Firelord.
The Fire Nation soldiers in the Earth Kingdom don't really look for him, they just kinda react when he shows up but no one is proactively seeking him out.
Even the Rough Rhinos, they are sent after Iroh and Zuko I think, and just decide to throw hands when they happen across the GAang.
Like... do we ever see this man actually assign someone to capture the Avatar? (Zuko doesn't count) Even Zuko hires an assassin after Aang, which is move than Ozai ever does.
Intentional or not, this shows just how over-confident and egotistical Ozai was, to not even really feel threatened by the Avatar's return.











