replicate the web page in a browser in another program

All I want to achieve is that when I browse web page in a browser (A), there is another program (B) that replicate everything in my browser. By everything I mean user login, etc. Currently the program (B) is a electron app that simply renders web pages.

I tried to set up a mitm proxy server and load every page that my browser (A) receives from server into my program (B). But HTTPS doesn't allow a proxy in between the browser (A) and the server. So that fails.

Another approach that I can think of is to record every user action in browser (A), send them to program (B) and let program (B) perform them so it ends up with the same web page with browser (A). But that approach seems a bit dirty.

I wonder if there is any other way to do this.