Does new React Context API trigger re-renders?

Here is an update for your questions based on the useContext Hook:

const value = useContext(MyContext)

When the nearest <MyContext.Provider> above the component updates, this Hook will trigger a rerender with the latest context value passed to that MyContext provider. Even if an ancestor uses React.memo or shouldComponentUpdate, a rerender will still happen starting at the component itself using useContext.

A component calling useContext will always re-render when the context value changes. If re-rendering the component is expensive, you can optimize it by using memoization.

So given below code example, components Number and Text will re-render with each context value change, as both directly contain useContext(AppContext).

const AppContext = React.createContext();

const Number = React.memo(props => {
  const renderCount = useRenderCount();
  const contextNo = React.useContext(AppContext);
  return (
    <div style={{ backgroundColor: `${randomColor()}` }}>
      Number: rendered {renderCount.current} times.
    </div>
  );
});

const Text = React.memo(() => {
  const renderCount = useRenderCount();
  const context = React.useContext(AppContext);
  return (
    <div style={{ backgroundColor: `${randomColor()}` }}>
      Text: rendered {renderCount.current} times. I rerender with context value
      changes!
    </div>
  );
});

const App = () => {
  const [ctxVal, setCtxVal] = React.useState(0);
  const [prop, setProp] = React.useState(0);
  return (
    <AppContext.Provider value={ctxVal}>
      <Number prop={prop} />
      <Text />
      <button onClick={() => setCtxVal(ctxVal + 1)}>
        Change context value
      </button>
      <button onClick={() => setProp(prop + 1)}>
        Only change prop in Number
      </button>
    </AppContext.Provider>
  );
};

function useRenderCount() {
  const renderCount = React.useRef(1);
  React.useEffect(() => {
    renderCount.current += 1;
  }); 
  return renderCount;
}

function randomColor() {
  const letters = "0123456789ABCDEF"; let color = "#";
  for (let i = 0; i < 6; i++) color += letters[Math.floor(Math.random() * 16)];
  return color;
}

ReactDOM.render(<App />, document.getElementById("root"));

<script src="https://cdnjs.cloudflare.com/ajax/libs/react/16.13.0/umd/react.production.min.js" integrity="sha256-32Gmw5rBDXyMjg/73FgpukoTZdMrxuYW7tj8adbN8z4=" crossorigin="anonymous"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/react-dom/16.13.0/umd/react-dom.production.min.js" integrity="sha256-bjQ42ac3EN0GqK40pC9gGi/YixvKyZ24qMP/9HiGW7w=" crossorigin="anonymous"></script>
<div id="root"></div>

Are updated to the context not propagated via the ususal rerenders? As I cannot see my logs / color changes when context changes.

The updates to context values doesn't trigger re-render for all the children of the provider, rather only components that are rendered from within the Consumer, so in your case although number component contains the Consumer, Number component isn't re-rendered, rather just the render function within the Consumer and hence the value changes on context updates. This way it is quite a lot performant as it doesn't trigger re-renders for all of its children.

Are all the consumers to that Provider updated or not ?

All consumers to that Provider will go through an update cycle but whether or not they re-render is decided by the react virtual DOM comparison. A demo of this you can see in the console for this sandbox

EDIT

What you need to make sure is that the components are rendered as children of the ContextProvider component and you are passing handlers to it instead of rendering them inline and updating the state of ContextProvider because that will trigger a re-render of all components that are within the ContextProvider

Performant usage

App.js

  constructor() {
    super();
    this.state = {
      number: Math.random() * 100,
      text: "testing context api"
      updateNumber: this.updateNumber,
    };
  }
  render() {
    return (
      <AppContext.Provider
        value={this.state}
      >
        {this.props.children}
      </AppContext.Provider>
    );
  }

index.js

class Data extends React.Component {
  render() {
    return (
      <div>
        <h1>Welcome to React</h1>
        <Number />
        <Text />
        <TestComp />
        <AppContext.Consumer>
          {({ updateNumber }) => (
            <button onClick={updateNumber}>Change Number </button>
          )}
        </AppContext.Consumer>
      </div>
    );
  }
}

const rootElement = document.getElementById("root");
ReactDOM.render(
  <App>
    <Data />
  </App>,
  rootElement
);

Less Performant usage

App.js

class App extends Component {
  constructor() {
    super();
    this.state = {
      number: Math.random() * 100,
      text: "testing context api"
    };
  }

  updateNumber = () => {
    const randomNumber = Math.random() * 100;
    this.setState({ number: randomNumber });
  };

  render() {
    return (
      <AppContext.Provider value={this.state}>
        <div>
          <h1>Welcome to React</h1>
          <Number />
          <Text />
          <TestComp />
          <button onClick={this.updateNumber}>Change Number </button>
        </div>
      </AppContext.Provider>
    );
  }
}