Let's concentrate on couple of countries to simplify the discussion: Iran, Egypt, Algeria. Water scarcity there is dominated by explosive population growth there in the last 70 years.

Water is not scarce in general, just yet. It scarce where population is exploding.

High birth rates in low-resource localities seems like a poor survival strategy.

Unless the new people are used as an army to take the needed resources from others...

I think it's both. Local populations adapt to whatever the local reservoirs can sustain but as soon as an unexpected climate event occurs (such as unusually low rainfall in a given season), the water reserves can no longer sustain the population. See Cape Town (2015-2018), Chennai (2019), São Paulo (2014-2015), California (2012–2016 & 2020–2022), etc.

If the local reservoirs were not already at capacity, or had much more redundancy, these events would have been much easier to manage. Fewer people in high risk areas would in fact reduce the risks of water scarcity.