I was playing on a 1.16.3 server with some friends and we all experienced some bugs concering mobs spawnings, that is:
Creepers and Skeletons spawning too close to players (1-2 block distance, or even directly on the same block)
One single magma cube spawning in the overworld
An unusual amount of mobs spawning inside walls (skeletons, creepers, zombies and endermen), both inside caves and outdoors
One evoker spawned outside, far from any village and mansion and not during any raid.
Related to the magma cube: we didn't build any nether portal yet in this world and it spawned close to y=10 depth (while digging straight 1block-wide/2blocks-tall corridors looking for minerals), Creepers and Skeletons spawned too close to players both in said corridors and outdoors.
We also expercienced mobs spawning in well-lit areas (such as the magma cube in the aforementioned corridor)
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As an update: we played again and we noticed other anomalies, such as mobs spawning in large groups (9 creepers, no other enemies) in well-lit areas, more mobs spawning inside walls (even into 1-block-wide walls inside our house, with plenty of room on both sides, and while it was surrounded by torches)
In the nether we encountered several mobs spawning inside walls, ghasts in particular, but also one blaze which spawned randomly without any fortress and died in a wall.
In the end we reverted back to 1.16.2 and it seems like those spawn-related bugs disappeared.
Moreover, we noticed that tamed cats stand still and do not follow the player, and instead teleport next to it as it gets very far away (this is present both in .12 and .13)
Please provide a screenshot of your game while you are on the server with the F3 debug screen enabled.