Do you code tests in you MVP or Beta release?

To begin with it depends on how many (if any) customers you have and what they are expecting.

When starting up I don't write tests while i'm more of a prototyping phase, throwing stuff together and changing things quite often, I think speed is very important there.

When stuff settles down a bit more I start writing tests, mainly focusing on tight and fast unit tests.

In my ideal world there would also be some integration tests for some of the main happy paths, but I don't have those yet.

I was in the same position. Ideally, we should all start with a test suite set up from the beginning, right? Well it took me deploying a dev key into production and completely using up all my free credits to make me realize I needed some sort of gatekeeper for deployment. I got a test suite set up that only checked one thing– that the key I'm using is pointed to production. Since then and as the product matured, I've been adding tests for critical features that cannot go wrong, such as 2fa, account set up and email campaigns. If I were to do it all over again, I would have set up basic testing from the beginning. Keep in mind you don't need 100% test coverage and some is better than none :)