Leaflet- marker click event works fine but methods of the class are undefined in the callback function

This is a classic JavaScript mistake.

this in JavaScript does not necessarily refer to your class instance object. It is the context of the function when it is called.

You can force this context with bind, and in many libraries you can easily force it as well. In this case with Leaflet you can pass a 3rd argument to on when attaching your event listener:

// Force current `this` to be the context when `this.markerClick` is called
marker.on('click', this.markerClick, this);

With bind it would be:

marker.on('click', this.markerClick.bind(this));

And there is also the arrow function solution, which uses the context / value of this where the arrow function is defined, rather than where it will be called:

marker.on('click', (event) => this.markerClick(event));