Thank you for your question about putting your spent PROMIX HP into your garden beds.  According to the Premier Company, makers of PROMIX products, the HP product contains 65-75% sphagnum peat moss, perlite, limestone, a wetting agent, a biofungicide (Bacillus pumilus (GHA180), and mycorrhizae.  

The limestone is used to raise the pH of the medium, and breaks down over time.  In the quantities from your microgreen growing it would not likely affect your soil's pH.  The wetting agent, used to facilitate water absorption by the peat moss, would also not be a problem.  

The biofungicide used in the HP mix is there as a preventative to protect the plant from fungal diseases.  It also can enhance root growth.  It does have a shelf life---a time during which these living organisms are alive---and it is unlikely that they would cause a problem in your garden beds.  Here's some information from the University of Massachusetts about biofungicides:
https://ag.umass.edu/greenhouse-floriculture/fact-sheets/biofungicides

Mycorrhizae are organisms that naturally occur in soils and bind with roots in a mutually beneficial relationship.  Those left in your potting mix would not likely harm your soils.

You asked about the accumulation of salts in the potting mix that might harm your garden beds.  Salts that build up in potting soils result from the use of fertilizers, which is why it is helpful to regularly water your plants thoroughly with plain water to wash these salts out.  Rains in your garden beds would perform the same function.

If the PROMIX HP that you are planning to add to your garden beds was initially used by you and you are sure there are no other chemical additives it would likely be safe for you to use as a bed amendment.  If you are obtaining the PROMIX HP from another source you should make sure to ask whether there have been any other chemicals added during the growing process.

Best of luck.

Thank you for your helpful input and references. 

The spent PROMIX HP was donated by a microgreen business to our community garden. Since it is primarily peat moss and perlite we assumed it would be safe to mix into our raised beds. Some of our more experienced gardeners have complained that their harvests are not as good as they used to be. We have asked if other chemicals were added but unfortunately, there's no way to ensure that we've received reliable information. I've decided to put on my citizen scientist hat and experiment with the spent product we currently have (several huge hills worth.)
I'll compare plant growth using the spent media itself with various combinations of spent media and garden soil and/or compost, and composted manure. Hopefully this will at least demonstrate if using the spent media is harmful in and of itself. If it does prove to be safe then we can determine what should be combined with to grow healthy plants.  Stay tuned.

Good for you for putting on your citizen scientist hat!  I think you should consider doing a soil test, and make a note to the testing lab that you are testing for pH and other factors in light of regular amendment with your potting mix.  Michigan State University, Penn State, and the University of Massachusetts all have good labs.  You might want to do so soon, since they get busy quickly in spring with home gardeners and farmers.

It seems unlikely to me that a microgreen grower would be adding harmful chemicals to their potting mix.  

There are so many variables that can affect gardening success (weather, watering practices, etc).  

Good luck with your investigation.