EMB-505 Captain reported on climbout a fuel pump and cross feed failure resulted in a fuel imbalance; an expeditious divert and uneventful landing.

Narrative

Departing ZZZ1-ZZZ2; on climb out through 12;500 'Fuel2 Feed Fault' advisory CAS (Crew Alert System) illuminated. QRH lists as 'advisory only'; auxiliary fuel pump activated automatically; and crew agreed to continue. Climbing though 42;000ft to level at 45;000; 'Fuel 2 Lo Pres' Yellow CAS illuminated. At 43;500 crew requested ATC for 43;000 as a cruising altitude to run QRH. During QRH checklist; 'Fuel Pump 2 Fail' Yellow CAS illuminated. Fuel synoptic page was referenced and two (2) yellow X's covered both Main and Auxiliary fuel pumps and it was noted that no fuel was being drawn from right fuel tank. Anticipating a fuel imbalance; crew agreed to divert to ZZZ and the request was made to ATC. While descending through 40;000ft the 'Fuel Imbalance' CAS illuminated at which time the crew [requested priority handling] and expedited decent. ATC requested fuel/souls on board and [gave] priority handling. While descending through 25;000ft the main fuel pump continued to activate intermittently; and fuel imbalance was stabilized at around 275 pounds and remained mostly unchanged until landing. Attempting to crossfeed fuel was unsuccessful. A normal landing was made; no damage to aircraft or injury to persons occurred. Multiple yellow CAS messages on PFD (Primary Flight Display)/Indications (X's) on fuel synopsis page.Cause: 'Fuel2 Feed Fault' 'Fuel 2 Lo Pres' 'Fuel Pump 2 Fail' 'Fuel Imbalance' CAS messages were caused by dual fuel pump failures on right side of fuel system. QRH was referenced regarding CAS messages; due to failure of fuel pumps a fuel imbalance was observed and decision to divert was agreed upon by crew. [Request for priority handling] was made and accelerated descent was performed to expedite deviation.Suggestions: Aircraft engine should be inspected for fuel/sensor/electrical faults.