I was going to say Napoleon Dynamite, but after reading your description, I’m going to say Napoleon Dynamite. When asked what time period it takes place in, the director said “Idaho,” which places it squarely in the post-apocalypse. Exploration? Yes. Adventure? Of course! Love and hope? Maybe. No spoilers.

Star Trek Picard kinda has me feelin the feels.

Castle in the Sky and Nausicaa kinda have those vibes.

Might not be the best fit but the first thing I thought of was The Wild Robot from 2024. Charming story and absolutely gorgeous visuals.

Others have already mentioned Station Eleven. I'd like to add The Last Man on Earth. It's more of a comedy series, but still somewhat fits.

Maybe Scavengers Reign? It has light and dark elements and rather than post-apocalypse, it is stranded space farers on an alien world. https://en.wikipedia.org/wiki/Scavengers_Reign

I haven't seen it myself yet, but I hear Station Eleven is about a traveling acting troupe 20 years or so after a pandemic-type apocalypse?

To honor the great actor that just left us (Tom Skerritt), perhaps something he starred in.

Although the one probably most fitting would be "Alien".

Has lots of the exploration, adventure and maybe even some hope (if you want to see the ending that way).
Not so sure about the "love" part. On the other hand, one of the stars is a cat!

The feeling is definitely somewhat post-apocalyptic, but also as non-cozy as it gets.

But for coziness, there also is "Picket Fences", so maybe a double-feature?

How about Andrey Tarkovsky's Stalker? Fittingly called a masterpiece.

I'm more of a shows person than movies and the first thing that came to mind was Silo, freaking loved it. Also Pluribus! :)

Not really cozy but here are some movies from https://en.wikipedia.org/wiki/Category:American_post-apocalyptic_films that I would watch:

• I watched Bird box recently, it was good.
• AI by Steven Spielberg
• https://en.wikipedia.org/wiki/Akira_(1988_film), it's been a while
• https://en.wikipedia.org/wiki/Fist_of_the_North_Star_(1995_film), I have never seen that one, but it should be as awesome/awful as the cartoon
• https://en.wikipedia.org/wiki/Logan%27s_Run_(film), never saw that one but it seems fun

https://en.wikipedia.org/wiki/Into_the_Badlands_(TV_series)

If you like musicals, Hadestown hits on all of those themes using the Hades/Persephone & Orpheus/Euridice myths.

It's a world gone wrong and it's up to the mortals to set things right.

Maybe The Shannara Chronicles?

Instead being set in the far future of an apocalypse leading to robot animals, it's more of an apocalypse set in the far future leading to Lord of The Rings:

https://www.youtube.com/watch?v=zIiymbl9ji8

Station 11