Will 11-speed SRAM RED eTap levers communicate with 12-speed SRAM RED, Force or Rival eTap AXS electronic derailleurs?

No, they will not.  11-speed SRAM eTap shifters are not compatible with 12-speed eTap AXS components.

On the other hand, Force eTap AXS and RED eTap AXS shifters will be compatible with 11-speed RED eTap derailleurs: Do SRAM eTap AXS shifters work with eTap 11-speed front and rear derailleurs?