I played on a Minecraft server, 2b2t, which has hundreds of people online, and generated some chunks for the first time to build a base. Mobs spawned in the newly-generated chunks, but after a while, they stopped spawning. Only hostile mobs spawned. I then built a mob grinder and no hostile mobs spawned in there, and I even double and triple checked that I had built it correctly. I do not know whether this is a problem in how far I go out, since I am super far out away from 0,0 XZ, or is it the TPS, since the TPS can go down to 0.75, which is extremely low. I really need to breed mobs, and without mobs, I cannot do this without going out about another 10,000 blocks, which is a very long journey, even if I use the Nether. Can someone please explain what is going on? Thank you.
First off, passive mob cap is very low - normally on vanilla it's 10 mobs world-wide and regardless of the number of the players, and typically already occupied by mobs in spawn chunks whenever the world generates. Passive mobs generate with new chunks ignoring the mob cap, but after that they can only spawn if the total number of mobs in all loaded chunks (including spawn chunks and whatever's permaloaded) is below 10.
On any typical server, you won't be getting any spawns unless you spawn-proof the spawn chunks - remove all the grass, and likely most of the sand (turtles / rabbits!) and kill all passive mobs in the spawn chunks. On an active server you won't be getting any spawns because other players load areas with passive mobs in them - including their own private farms, animal pens, mounts, pets etc.
Low TPS would reduce the spawn rates (normally new passive mob spawn attempts occur 400 ticks apart, so 20 seconds on normal servers, but at 0.75tps that's once per 5 minutes) but it wouldn't block spawns completely. Distant location is non-factor. But the number of players online means there's way more than 10 passive mobs loaded at any time, and so no new spawns. It's best to give up on hoping to spawn them and breed your own from naturally generated instead.
Because you are playing on 2b2t, which has a lot of people online, mobs try to spawn around everyone when they can which means that mobs rarely spawn and mob grinders don’t work. Basically if a pig wants to spawn, it's got over 200 people to pick from and the chances of it picking you is less than 1%.