Thanks, I never really knew that this is what active monitor really means

I guess next time I should be looking for something like this:
"Active crossover network with 4th-order Linkwitz-Riley filter"
I can't say you misused the term. Powered speakers are commonly referred to as "active".
But when somebody like TLS Guy is saying all modern speakers should be active, he is saying the crossover should be upstream of the amps. Otherwise, a lot of power gets wasted as heat at the crossover.
I don't know if this statement is valid, but it makes intuitive sense to me to manipulate the low level signal and give the high current amplified signal a clean and straight shot to the drivers. It also allows a manufacturer to customize the amp to the driver.
For example, my Focal Solo6 Be uses a 150WRMS class D amp (efficient good slam, but not good for high frequencies) for the woofer and a 100WRMS class AB amp (good sound, but inefficient - source of heat) for the tweeter.
I doubt the B2031A offers the full advantages of the active format, but within the cost constraints, I suspect they did what they could.