Thanks for the new bug discovery! I've done some experimenting and it appears that this is solely about monitors, not crates or barrels, and occurs solely in servers (including single player servers), not local multiplayer. Here's the level I've been testing with, so we're all on the same page. I found it also useful to test what happens when the floor disappears from under a monitor twice.

There are a range of behaviors here across different versions and in different contexts, so I'll try to list them here.

Local Games:
Vanilla to 4.3: Lands properly and retains its previous vertical speed for the second fall.
5.0 to 5:11: Lands properly and resets its vertical speed to 0 before the second fall.
5.12: Lands properly and resets its vertical speed to 0 before the second fall.

Servers:
Vanilla to 4.3: Lands properly, but stays floating in midair instead of falling a second time
5.0 to 5:11: Lands properly and resets its vertical speed to 0 before the second fall.
5.12: Falls through the floor!

For trigger crates, the difference between resetting vertical speed and retaining vertical speed matters: that's how animated tiles can be used to open falling crates. For monitors, I don't think it matters from a gameplay perspective, it should just be whatever people think would be better.