There is the possibly of a new hit region api in canvas that can be used as a way to define additional interactivity for objects that are drawn in a canvas. As of this writing there is very poor browser support for this, in fact it does not seem to work at all in any browser that I use at least.
I do not think that a hit region area should really be the responsibility of a canvas drawing api any way, and that a canvas element does not need to be a replacement for other HTML elements. Sure the subject will come up often, but hit detection should be a part of the class, model, framework or whatever it is that you are using outside of just the canvas element and the drawing api alone.
One way to make it so you have a hit area in the canvas is to use a basic bounding box collision detection method. This kind of method should be a part of a framework that you are using, if you are just going vanilla js style though you could start out with just something like this maybe.
A method such as this can be used to find out if one box area overlaps another, and can then be used in conjunction with many other methods and objects to create, and mutate a state. That state then just needs to be rendered to the canvas.
Now that I have covered how to have a simple bound box collision detection method, I can now use that to make it so that when and area of the canvas is clicked that results in some kind of action. In this section I have an example that uses the bounding box method to know that and area is clicked and when such an area is click I cycle over some indexed color values for that area. In other words when the area is click it changes color, not the most interesting example, but it is a start when it comes to this sort of thing with canvas.
I can not say that this is the best way to go about setting up some buttons in a canvas project, but you get the general idea. A hit detection method can be used to find out of an object was clicked or not, and then some kind of action can be preformed. In a real project I might go about pulling code like this into a module of sorts, and also make the objects a little more flashy.