A variable displacement pump is what both the L84 5.3l and L87 6.2l engines have, but a variable displacement pump is not functioning as a 2 stage pump. The "2 stage" pump uses an electrically operated solenoid to likely bleed off oil/oil pressure back into the sump when engine conditions are not requiring as much oil pressure/volume. This is likely why there are 2 different oil pump part numbers, one likely with a 2 stage solenoid and one likely without the 2 stage solenoid. It may be possible that the 2 stage solenoid is not a serviceable part by itself as I have not been able to find one.Pumps are not interchangeable but you'd think they were looking at them. Both are "2 stage" as in they're both variable geometry pumps. GM does reference the L84 as "single stage" but it's more marketing than anything else. In theory they're infinitely variable but GM only uses a binary high output and "low" output via the solenoid.
For reference, for the previous generation 5.3l L83 and 6.2l L86 they actually did use the same oil pump based on part numbers I have found and I believe both these engines had the 2 stage oil pump solenoid.
All the research I have done and it has been quite a bit indicates that the current generation L84 5.3l engine does not have the 2 state ECM controlled solenoid like the L87 6.2l currently has. As mentioned, research seems to indicate that the previous generation L83 5.3l engine did have the 2 stage oil pump that was ECM controlled.