There is datetime-local, date, and time. And there's a lot of control over what is allowed with min-max ranges, steps, etc.
The only thing I can imagine to go wrong here, is when a user has their browser set in US-en but when they are not aware of that. Which seems... weird; or at least not a problem a web-dev should solve.
> Lets you enter nonexistent dates like 31/2
This may be an issue in specific browsers/versions/os. But enabling the "validation" by setting required and/or some other attributes, gives an error for these dates AFAICS. But, in any and all cases: server-side validation is needed anyway. You just cannot trust a value sent by a user, whether that's "validated" with sixty npm-packages and their dependencies, or by the browser.