I don't think Harry is romantically interested in Hermione, he still thinks kissing is icky, etc.

I figured Harry gave Draco and Hermione the potion because he wanted them to triumph over him together, but in a really dramatic challenging way. If their triumph was hard-fought and dramatic they would be more likely to bond over it. Once Draco was friends with a muggleborn, he would be forever lost to the blood-purists, and Harry would have one a great victory. That is what Harry cares about the most. He obviously is willing to lose to let it happen because he engineered the Dramione alliance from the beginning.