I’m sorry but framework and library in this post are going to be used loosely, because even React, Vue, Angular, Svelte, etc devs use the terms loosely.

React is mostly a UI library like you would find in most native app development. Of them all them JS frameworks/libraries is one of the less opinionated and with less batteries included. By design it does not does everything. Most other frameworks do way more.

It lets you define custom components. The components can have properties that their parent component defines and internal state. If the state or the properties change the component gets redrawn (magically). There are some lifetime functionalities (things to do on first render for example) and performance improving stuff (memoization) but mostly that’s it.

All the other features you talk about are third party libraries or frameworks that can operate with react or are build on top of and cover the bases, like routing, fetching, caches, server side rendering, styling utility libraries, component libraries, animation libraries, global state management, etc.

The big difference with the vanilla way is that the approach is mostly declarative. The runtime takes charge of updating the DOM when your components state or properties change.

You take a big performance hit, and an even bigger bundle size one, but the speed of development and huge ecosystem of readymade solutions can be really important for some use cases.

Other frameworks take different approaches to solve the same problems:

Component system for code reuse and organization.
Some way to manage state
Some way to decide what to re-render and when.
Extra stuff. Some frameworks end here, some have tools for everything you would need for a web app.