feedback for duplicate registration attempt if a user tries to register with a username or email that is already in use, there is no feedback telling them this, it just highlights the form field red, this is quite a bad UX.

How can I add translatable text to the effect of "that email is already in use, have you forgotten your password?" ?

I would really like to do this without adding a module.

Here you can see there is validation feedback, but it's not relevant, as my username meets its criteria, it should highlight the duplicate account problem. The user would just get frustrated at this point as they are told to do something which makes no difference.
It sounds like your theme is missing  from the page template, which will usually show a description of the error at the top of the page.

I know you said no modules but I would recommend looking at Username originality AJAX check which is very small and does an ajax lookup before the form is submitted.