As a supplement to @uhoh's answer, I would suggest Collateral Damage to Satellites from an EMP Attack as a reference point. This does not discuss direct impacts on astronauts, but instead is focused on radiation effects on satellites, or, as put in the abstract "this paper examines the potential damage to satellites from high altitude nuclear detonations not specifically targeting space assets."

Further in the abstract:

We conclude that LEO satellites are at serious risk of exceeding total-dose limits for trapped radiation if generally accepted natural space hardening criteria are invoked. We believe, however, that the probability of an individual satellite being sufficiently close to a detonation to be threatened by prompt radiation effects is relatively low. GPS and GEO satellites are threatened only by the very high yield (~ 10 Mt) detonations

They consider separately

threats from "prompt" weapon outputs and from "induced" environments, including long-term trapped radiation ("pumped belts").

Here, prompt is immediate effects from the burst. Pumped belts are a result of charged particle injection (lots of beta decays in fission products!) into the Earth's magnetosphere, resulting in lots of charged particles flying around in space.

In the conclusions the authors note

• ll satellites in LEO are at risk to serious damage from line-of-sight or enhanced radiation belt exposure resulting from EMP attacks over many geographical locations of the Earth.

Earth's atmosphere and the ephemerae of LEO satellites reduce the probability of line-of-sight irradiation to less than 20% for many threat scenarios, rendering the immediate loss of a few satellites a distinct possibility. The pumping of radiation belts constitutes a serious long-term hazard to all LEO satellites.

So, prompt to longer term (months) degradation of electronics, most notably the solar panels of the ISS, could well render the ISS uninhabitable well before running out of supplies.

As a supplement to @uhoh's answer, I would suggest Collateral Damage to Satellites from an EMP Attack as a reference point. This does not discuss direct impacts on astronauts, but instead is focused on radiation effects on satellites, or, as put in the abstract "this paper examines the potential damage to satellites from high altitude nuclear detonations not specifically targeting space assets."

Further in the abstract:

We conclude that LEO satellites are at serious risk of exceeding total-dose limits for trapped radiation if generally accepted natural space hardening criteria are invoked. We believe, however, that the probability of an individual satellite being sufficiently close to a detonation to be threatened by prompt radiation effects is relatively low. GPS and GEO satellites are threatened only by the very high yield (~ 10 Mt) detonations

They consider separately

threats from "prompt" weapon outputs and from "induced" environments, including long-term trapped radiation ("pumped belts").

Here, prompt is immediate effects from the burst. Pumped belts are a result of charged particle injection (lots of beta decays in fission products!) into the Earth's magnetosphere, resulting in lots of charged particles flying around in space.

In the conclusions the authors note

• All satellites in LEO are at risk to serious damage from line-of-sight or enhanced radiation belt exposure resulting from EMP attacks over many geographical locations of the Earth.

Earth's atmosphere and the ephemerae of LEO satellites reduce the probability of line-of-sight irradiation to less than 20% for many threat scenarios, rendering the immediate loss of a few satellites a distinct possibility. The pumping of radiation belts constitutes a serious long-term hazard to all LEO satellites.

So, prompt to longer term (months) degradation of electronics, most notably the solar panels of the ISS, could well render the ISS uninhabitable well before running out of supplies.