We may be looking at the term "Presidential" in different lights. Asking a reporter to pull your finger then letting out a loud fart is not Presidential. Meeting foreign dignitaries and heads of state in foreign lands to discuss affairs of the world is Presidential. At least in the sense of what is required of him to carry out his sworn duties.
No doubt it was a photo op. One of the best I've ever see. There's Putin who is arguably on the ropes with a major speech scheduled for tomorrow and expected to tell his propagandized allies and his own citizens how well the war is going. Before he gets the chance there's the US President and the Ukrainian President standing side by side smiling on the steps leading to Kyiv's Governmental Headquarters. And this, in a city that is coming under attack from time to time. Vlad has probably been rehearsing his speech for weeks then on the eve of delivering it he has to make big changes in light of how heavily the world has covered Biden's trip. I'd say Biden delivered a bit of a sucker punch.
Agenda? I think the photo op above and Ukraine being at war with a world power that happens to be one of our biggest adversaries is enough to justify the trip and talking face to face about it.