Will a new SRAM RED AXS™ road chain work on a SRAM Eagle™ drivetrain?

No. SRAM EAGLE™ chains and SRAM RED AXS™ chains have different dimensions and are not cross compatible. The derailleur, cassette and chain should always “match”. When using an Eagle™ cassette or derailleur, use a matching Eagle™ chain. When using a SRAM RED® cassette and derailleur, use a SRAM RED® chain.