feat(examples): Migrate 'with-mongoose' example to TypeScript with total type safety (#53603)
### What?
I kindly request the maintainers to review this Pull Request, which aims to migrate the `with-mongoose` example to TypeScript with total type safety.
### Why?
By doing so, we enhance the overall quality and maintainability of the example, aligning it with modern best practices for type-safe codebases.
### How?
I have thoroughly tested the changes to ensure they do not introduce regressions and maintain compatibility with the existing codebase.
Co-authored-by: Balázs Orbán <18369201+balazsorban44@users.noreply.github.com>