Mulch with guar or xanthan gum added to bind nutrients and water, turns into a gel when wet, stays wet longer.
It's what they use in the hydroseeding straw and fiber. Doesn't look like you have leaf or grass mulch around...get bales of straw.
There's a certain order to mix to encapsulate the nutrients into the polysaccharide gum. Looks like plenty of iron in the soil, so Calcium goes in first, gets turned into micro-encapsulated calcium carbonate, then other base nutrients can be added/encapsulted if needed.
If you don't add calcium, then it strips calcium & iron out of the soil.