nit: can be merged into one

Copying part props from input.react.js is something I would like to avoid. (eg. what is type there will change in the future?)
I would suggest exporting that type and defining this one using type utilities e.g. $Rest - it's not the best for readability but I would avoid splitting props type in input to baseProps and additional because right now it represents cohesive whole.

At first sight, it looks like some sort of magic strings, which is not clear to me, but I get this is a prop to standard HTML <input>.

I am not sure what will be better, eg. adding special type for this:

const passwordInputState= Object.freeze({
  passwordHidden: 'password',
  passwordVisible: 'text',
});
export type PasswordInputState = $Values<typeof passwordInputType>;

will improve complexity so probably it's better to leave this as it is.

We are in a functional component, each time component will re-render function will be redefined, we could improve this by using React.useCallback

Looks like there is no need to use a function - you can use a simple constant here (probably wrapped inside React.useMemo).

Let's move the spreading operator to the first place to prevent overriding type (if you think there will be a use case in the future where placeholder will be overridden from the parent component it's okay to leave it before spreading).

type={type} can be shortened to type

nit: shorthand

in case of 0px unit is redundant

I am not sure there is a need to add Wrapper suffix everywhere, we could e.g. rename fieldsetWrapper to wrapper since it's the main responsibility and find a more appropriate name for others but it's up to you.

More often in codebase, I've seen passing size as a number

sounds good to me

According to line 14 in this file, this padding will be applied to both password and text input (where there is no icon), is it an intentional change? If now I would suggest apply this padding to place exactly where we have input + icon which is password-input.react.js

For me, it's confusing because I will see a wrapping login and an empty space on the right side.

This selector is probably not what you intended. Instead of selecting .wrapper when in hover state, it selects all the descendants of .wrapper which are :hover. If it was intentional, please explain why we're doing something like this, as this might be bad for maintainability.

Why do we need this?

We can be more specific with the type

Do we really need to use setHtmlInputType as a dependency? Does this ever change?

What is the benefit of memoizing this value?

I'm not sure if these two need to be mandatory. Can we make them optional?

We should use classNames library to merge classes