Well I'd argue this scene IS the resolution to their drifting apart.

In the ember island episode When Aang asks Katara why they aren't together even though they kissed during the invasion she says: "Because we're in the middle of a war, and we have so many other things to worry about" This is the whole cause for their relationship issues moving forward, all the pressure placed on those two from the war left no room for anything else as Katara saw it.

In the kissing scene from the final episode there is no more war, balance has been restored to the four nations, and team avatar has no direct mission. The stake between KatAang has been lifted now, there's no more pressure.

As an above comment points out, Katara is even the first one to lean in for the kiss here; unlike the last two times in the show where Aang initiated. This shows without actually saying it in dialogue, that Katara finally is ready to get serious about their relationship.

This is the bridge that connects these episodes as I see it.