Which aspect of the postwar era did jazz’s liveliness, looseness, and improvisation most reflect?

I would say disillusionment. During this time, many people were faced with the brutal realities of war. It was no longer a thing of glory; soldiers died in new terrible ways. This is also reflected in the poetry and prose written during this period. Improvisation arose as a result of the old ways of thinking being broken down. Looseness and liveliness resulted from old traditions being dissolved. Hope this helps.