is there an example of password recovery by mail?

don't know if this helps, but you can look at the node-advanced graphql boilerplate (google it) and then check the signup/login authentication based on jsonwebtokens. you could then use this same approach to create a jsonwebtoken that is sent to a user via email upon her request. when the user provides this token (by clicking on the link in the email), you check the expiry date and maybe if the password has changed since (to invalidate the token once it has been used). if it's all ok, you allow the user to change her password

Thinking that this function is necessary for everyone and can already have a ready solution?

prisma, graphql, node, etc. they provide the buildings blocks for you to build these things. if you don't want to build it, you better of using a CMS that has pre-built modules that do these things for you

It is surprising that I did not find in the Internet training materials on this task