Why is the spacesuit design so strange in Sunshine?

It seems to be specifically tailored for its use in close proximity to very high solar radiation. Remember that the team in Sunshine has to operate in very high sunlight and the dangerous effects of the sun are a major motif of the film, which the design of the spacesuit reflects (pun intended) very well.

The golden foil plating is supposed to reflect most of the incoming heat radiation and is similar to the common space blankets employed e.g. by fire rescuers or ambulances. And the very thin visor reduces the visor area (which is itself more sensitive to radiation, not to speak of the vulnerability of the eyes) as much as possible while still providing the wearer with (at least minimal) vision.

It also appears to be inspired by the suits used by foundry workers and industrial firefighters for working in close proximity to intense radiant heat. Here the suit is constructed from some heat resistant fibre such as nomex, Kevlar or glass fibre and coated with a thin layer of aluminium which is effective at reflecting away radiant heat without adding too much weight.

Note that these suits are very much about protecting against radiant heat rather than direct contact with flame (where the suits worn by racing drivers and combat pilots would be a better model).

I think the narrow vision slit has to be put down to artistic license to some extent.

The closest modern analogy for the vision slit is welding masks which have to protect against faily intense UV and IR radiation and tend to have a fairly restricted field of view but even the it tends to be a lot closer to square than a narrow slit.

The thin visor is an example of https://en.m.wikipedia.org/wiki/Snow_goggles . Snow goggles are used to prevent snow blindness, from sun light reflecting off the white white snow. Mainly, it reduces the amount of UV light which is the damaging aspect of sunlight. The small slit controls the amount of light that can get in. Tunnel vision does happen with it, but it prevents burning out your corona or retinas. Good trade off I guess. It also helps prevent snow from getting in your eyes. The same is done in the desert for similar reasons.

When commercial protection like sunglasses are not available, some survival guides suggest making these snow goggles from a dark cloth.

In the movie, the spacesuit is tasked with protecting the user from extreme exposure to the sun. The slit, even in conjunction with UV blocking glass or other technology, would help reducing the risk of flash frying the eyes. UV glass alone may not be enough that close to the mega nuclear reactor that is a sun.