There are some reviews of the craftsman branded version of the same pump.  Buried in the comments are rare complaints about the priming.  Most animals seem to use them once, get good results, & throw them away.

The goog finally rediscovered the super expensive sprayers of past searches.  They would be ideal.

https://www.amazon.com/Chapin-75004-Electric-Rechargeable-Portable/dp/B0CY6QXFG2/

https://www.amazon.com/Electric-Plant-Spray-Bottle-Watering/dp/B0989ZHXFV

https://www.amazon.com/SOLO-260-Battery-Powered-One-Hand-Sprayer/dp/B0CPMDCTG2

Somehow these manage to cost $20-$50 & they still sometimes die.

Surprised even his $50 solo 260 failed to prime.  The shorter hose didn't matter.

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After blowing into the intake, the HDX sprayer eventually consistently primed when fed from a tank above it.  It might be prone to surface tension blocking the narrow passages, which is cleared by blowing into it. The valve seemed to hold priming after being lubricated.  The problems with these suction sprayers all seem to be surmountable with enough manetenance.

The mane problem is lack of space to store a large tank, large pump, hose, & standalone nozzle.  It's more important for it to be user serviceable & compact than manetenance free.  The experiment showed a motorized pump is really important to spray enough water on the hottest days or you're going to be making more heat from pumping.

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The most popular sprayer seems to be

https://www.amazon.com/HIFAY-ES1-Fertilizer-Rechargeable-Automatic/dp/B0BQBMC3XY

But the HDX sprayer has worked well enough to do the job.  The tendency of the $25 ones to need manual priming & break is a big negative.