For my post-post-apocalyptic world, the main feeling I’m going for is hope. The idea being that some time far in the past a great calamity happened, but humanity has rebuilt, and despite all the great setbacks nothing can stop people from reaching ever higher (indomitable human spirit, etc, etc).
Another feeling I’m going for is the sadness of knowing that some ancient civilizations are lost, and we have no records of them and how they lived, and these things that were so important to people of the past are just gone forever. In my world the knowledge of the old world from before the apocalypse is fading, their buildings are eroding away, stories of them are slowly warped until they’re unrecognisable, and the artifacts left behind are lost one by one.
I guess these combined also creates a theme of moving on, though I don’t think that counts as a feeling.