I doubt it will be "copyright infringement" since the code was rewritten. It might fall under patent infringment if something was patented.

The more likely scenario is that it will constitute a misuse of trade secret either under law or from the contract signed on employment. I am not a lawyer and the law is different in every place but it is likely that such a use would be protected under paw by protections given to professionals to retain expertease gained while practicing their professions. I don't remember how that protection is called.

Your employment contract or a related document you've executed may include a post-employment restraint/non-compete. These vary a lot by level of the position and type of work. They are difficult/expensive to enforce and are open to interpretation about "reasonableness". These are generally the former employer's best means to prevent you from immediately reproducing something. However they also can't prevent you from working in your profession and using what you've learned as a professional.

are there a lot of companies in the practice of copyrighting their internal architecture and patterns?

In usa everything that is copyrightable, becomes copyrighted at moment it is created. For instance that sentence, and this on, are protected works owned by me. The only reAson HN can legally use then is cause I gave them license, buried somewhere in Eula/site terms of use.

Also, an architecture is not copyrightable. Maybe patentable. Copyrights protect specific expressions, not a general idea, plan, or architecture. At least not yet thankfully I haven't seen anyone try to argue an unrelated software doing same thing is a derivative work.

But Twitter has a patent pledge with its engineers [1]:

    The IPA is a new way to do patent assignment that 
    keeps control in the hands of engineers and designers. 
    It is a commitment from Twitter to our employees that 
    patents can only be used for defensive purposes. We will
    not use the patents from employees’ inventions in 
    offensive litigation without their permission. What’s
    more, this control flows with the patents, so if we sold
    them to others, they could only use them as the inventor 
    intended.

[1]: https://blog.twitter.com/2012/introducing-the-innovator-s-pa...

Many big companies will patent their internal architectures. I've been involved in the creation of quite a few patent applications of exactly that. My name is even on one of them.

It's silly and ridiculous but necessary because of the way patents are enforced.

I can promise you that the existence of the patent system did not motivate us to build any of that software, but it certainly motivated us to patent it after the fact, so that someone else couldn't patent it and then sue us for having independently built the same thing.