What solutions available for a CMS-agnostic contact form?

By principle, I normally work with two different companies for establishing websites for myself:

• One for domain registration and domain-sole email address
• One for web application hosting

My problem

I have the problem that I don't want to use any contact form plugin/module/extension dedicated to my own CMSs because I like to use CMSs core-only (from various reasons but especially because it makes constant version upgrading very easy and promises more stability than otherwise).

I can just ask "how to solve that problem" to prevent an "XY problem" but to be honest I have done lots of research about this and I have found the window of solutions to be quite narrow.

The solution I seek

I seek a content management system agnostic (CMS-agnostic) solution for contact forms.

I thought about:

• Using some contact form outsourcing service (which costs money and there aren't many, or at least I am having hard time finding such services thorough Google)

• Learning how and creating some PHP file with a form (I happen to only work with CMSs which are mainly developed in PHP), hardcoding my email address in it, putting it in my website directory and referring it from my main menu somehow (my Apache webserver will serve it as HTML without my email in source code I guess)

I am not sure if these are my only options.

My question

What solutions available for a CMS-agnostic contact form?