Initially, I tried to if/else portions of the code to accommodate for
`MessagePort`, aiming to avoid duplication of the code (like I did for
`shared/frame-rpc.js` #3565). However, I found that, unlike
`shared/frame-rpc.js`, this resulted into a spaghetti-type of code, not
very understandable.

Then, I decided to create two internal methods to support both the
current communication using `Window` and the new `MessagePort`. This in
my opinion leads to a clearer results, although some code is duplicated
in both methods.

This PR will result on a reduction in code coverage, which will be fix
by #3590.