UPDATE 1: The issue seems to be solved after I set the world to Peaceful, waited a few in-game minutes, and returned it to Hard. THIS DOES NOT RESOLVE THE ISSUE, SEE BELOW...
UPDATE 2: Using the trick above doesn't last. A few monsters spawn, then nothing. It doesn't matter how far I travel, or how many sleepless nights, monsters never spawn anywhere.
UPDATE 3: A few things I've tried with limited success: I've tried reducing the simulation distance, and matching, reducing, and increasing the render distance of both computers. It seems that sometimes when I'm far away from the other player, I get some monsters spawning (most are Drowned), and she'll have a few spawn. The number of mob spawns aren't anywhere near normal, with a single Phantom sometimes appearing, but usually not, and we never sleep. Deep dark caves are utterly empty. Stone blocks that are supposed to spawn those cave critters break apart super-fast but without any critters appearing at all. ALSO PLEASE NOTE I DO NOT USE MODS.
Again, if only I am logged in, monsters abound everywhere in scary numbers, and often right in front of my face which has never happened before. It behaves almost like they were there the whole time, but invisible or disabled. With the 2 of us, there are virtually no monsters at all - we have to look for them, and usually find nothing, or at best a couple Drowned zombies.
UPDATE 4: I've reinstalled the game, and tried 2 new worlds - one just single-player, the other multi-player. Both worlds had only the initial spawn of monsters, with no new monsters spawning (except Drowned). No other monsters spawn.
UPDATE 5: I have found that if I toggle the Multiplayer option off/on, that a few monsters begin to spawn, however, these monsters often die immediately upon spawning. Endermen dying for no reason, the stone critters dying instantly upon being disturbed, etc. Even in this state, mob spawns are rare.
The amount of Drowned spawning seems unchanged from prior to 1.9.0. There are no unusual mass-numbers of them.