Phaseshifting is Angel's Siren power. As Lilith can Phasewalk to navigate the battlefield safely, and Maya can Phaselock an opponent to immobilize them, Angel can Phaseshift. This allows her to almost instantly and effortlessly interact with any technology in a network she is connected to, for various effects depending on the technology she's connected to. Throughout the Borderlands 2 storyline, Angel uses her power to interface with Hyperion technology, or electronics that are connected to Hyperion equipment. Each time Angel Phaseshifts, she announces "executing phase shift."
While Angel appears to possess the ability to digistruct ammunition for the player character in her control core, it's very likely that she does not possess the actual ability to do so, but instead used the existing technology in her control core to digistruct the ammo. Hence, it can be inferred that Phaseshifting's abilities, while seemingly endless, is limited by the capacity of the technology at the wielder's disposal.
It is revealed in Borderlands 3 that shortly after Angel's death, the Phaseshifting power passed onto Patricia Tannis, who hid the power in order to avoid any more scrutiny than she already attracted (As she was already a leading researcher on Eridian civilization and artifacts). Upon being kidnapped after absorbing the The Graveward, she is scheduled for execution in Carnivora, but upon the Vault Hunter's assistance, utilizes Phaseshifting to free herself and deliver Pain and Terror to their knees for the Vault Hunter to finish off by causing their machine to smash itself against various surfaces until it smashed itself to pieces.
The sidequest Childhood's End in Konrad's Hold both elaborates on the technopathic nature of Phaseshifting and the events (previously hinted at by both Angel and Handsome Jack in Borderlands 2) that caused Angel to eventually be imprisoned by her father, primarily due to her lack of control over her powers at a young age combined with an unfortunate outburst of emotions.