If you're looking for anime similar to Banished from the Hero's Party, I Decided to Live a Quiet Life in the Countryside (Light Novel), you might like these titles.
When this overworked office lady finally meets her maker, she’s reborn with an adorable ability. Midori is reincarnated in another world as a young girl, Nema, and must help decide if the humans there should continue to exist. In return, she gains the power to be loved by all nonhuman creatures. From fantasy beasts to mythical monsters, she’s free to pet any animal to her heart’s content!
Banaza, a humble merchant, is summoned to another world as a hero candidate, in the hopes that he has what it takes to defeat the demon army. When his summoners discover that he possesses no special skills, Banaza is summarily dismissed…but something goes wrong, and he can’t go back home. Now he must find a way to survive in this new kingdom. Luckily, Banaza might be more powerful than anyone–including Banaza himself–realized!
When Sasaki brightens up his tired corporate life by buying a pet sparrow, he never imagined the bird would actually be a reincarnated sage from another world! With his new avian roommate teaching him all sorts of magic tricks, could this be Sasaki's chance to escape his droll office job?
A Thai foreign exchange student named Mei finds herself bewildered when she first arrives at Saga station. She gets on a bus and, through interactions with the residents of Saga wherever she goes, she makes her own "precious memories."
Dariel is a soldier in the Dark Lord's army who cannot use magic. Instead, he wields his intellect and initiative as an assistant to one of the Dark Lord's most trusted captains. But when the captain is summarily replaced, Dariel also loses his privileged position and is fired. In disappointment, he retires in a village of humans, getting a new start at life by using his abilities to accept requests for help.