>>46220709JN49 (Eevee) is the culmination of all of these points. She's always been altruistic but it was hidden by her coldness. But now that that's been cracked by Ash and Gou showing her just how cool Pokémon are, when Yamper shows her this Eevee and shows her that it's being targetted, Koharu steps up to protect it, calling Gou to distract them and running off with it.
The real significance of Eevee and the reason that she ends up wanting to keep it though is because Eevee is like her: they both have a lot of paths ahead of them and they're both not sure what they want to do in the future. Koharu catches Eevee as her first Pokémon and vows to walk with Eevee one step at a time as they discover what the future has in store for them.
50 (Galar Fossils) has her follow up on that immediately, getting excused from school (on the condition that she writes a report about her experiences) because Eevee wanted to go see what was happening in Galar after the Pewter Museum Chief told them about it. 52 (Diglett) she goes because Endo the Farmer is a family friend and her father asked her to (and, assumedly, she didn't have school that day since she showed up in her overalls outfit instead of her school uniform). After the experience of helping him out, she shows that she's becoming more like Ash and Gou by mirroring how they acted at the beginning of the episode.
This leads into 55 (Ponyta) being the first time she's independently interested in a Pokémon since sometime before the series began, and she has a solo adventure where she has fun with all the Pokémon in the Glimwood Tangle. It shows just how far this transformation has come, starting with someone who couldn't care less in the current day all the way to someone who has an adventure bonding with Pokémon.
And that's all my autism about her character arc. It's honestly not that difficult to grasp. This is a kid's show after all.