The high pressure pump is supplied fuel via a low pressure lift pump, if there is not enough primary pressure the high pressure pump will not deliver enough fuel.

I would start by confirming primary fuel pressure/flow.

 

Seems he has the opposite problem. Fuel rail pressure is indicated as too HIGH (P0088), not too low.
Usual suspects:
Fuel pressure sensor no good, reading incorrectly - get lucky and it'll be this one
High pressure fuel pump - hope it isn't that, and probably won't be. Could easily run $700+
Volume sensor - not that likely, but on the list of potential sources

 

I have seen codes and alerts over the decade(s) on my vehicles. Many related in the end to the gas station I used once too often. Switch to a true name brand source Eg Exxon, Mobil or equiv as they top tier suppliers as well pump quality fuel. Shell is another if you have it there.

I'll add that after making that change and not going back to where I thought it was a result of or brand. The codes have never returned for many tanks and thousands of KM. How its related I don't know but I had no driveability issues just engine light and code of something quite wrong in the engine. Nothing else was done either.

 

The trucks that deliver to gas stations ALL pick up from a local terminal, usually on a major pipeline. The truck driver adds a pail of branded advertising magic (these days he pushes a button). The gasoline he adds it to is known as RBob. It is a generic product with a long list of EPA specs that it adheres to.

Ethanol is added at the terminal and arrives by rail since it is bad for pipelines and valves - picks up trash and water.

Regular gas can have up to 5% by volume of anything in it, transmix: kero (jet fuel), diesel, etc. Often they blend in butane when it is cheaper than gas. Premium gas is 100% gas, when it is even slightly tainted it is downgraded to regular. This is not secret knowledge.

Use your google maps and look at the sat pics for Doraville, GA for example.

Doraville, ga colonial

www.google.com