While I know its not housing, there's a shortage of self storage in my area.

Currently there is a sever shortage of single family homes in Seattle and the surrounding areas. 

@Mark BurkeYes, shortages are nationwide.

Housing shortage, builders can't keep up with demand, not enough lots are available and Interest rates are low. 

The supply of homes for sale fell 29.5% year over year, the largest annual decline ever, to 1.03 million homes.”Indeed, according to CEPro, SFH construction weakened 10.3% in February due to labor and material shortages.

It then rebounded dramatically in June and July, as consumers rushed out to buy suburban homes, seeking more space for working and schooling from home.Builders now say they continue to see a steady stream of buyers, due in large part to the extreme shortage of existing homes for sale.

The rate of inflation is the highest level in nearly 13 years, signaling greater stress on our economy as businesses grapple with supply shortages (that are at least temporarily raising the cost of many goods and services).

You can ask for the HAP contract and most recent lease amendment, both of which are documents the Housing Authority should have.The other issue is practicality - if your area is like most across the country, there is a huge shortage of housing where the landlord will take the voucher so what this means is that it is often difficult for the tenant to find a new place quickly. 

Is it supply and demand, rising housing prices, housing shortage or all the above or something else?  

On top of skyrocketing prices, there has been material shortages, so it may require settling for what is in stock or risk a delay in completion.