Minecraft – Why isn’t the Minecraft wither skeleton farm spawning any wither skeletons

This depends on many factors, including your position as a player and the type of terrain around you.

Mobs will despawn when they are out of a 128 block radius of the player.

This means that for the spawner to be active if the player is anywhere within 128 blocks at the spawner's level, it has to be at least 128 blocks above the ground. This works for pretty much any generic mob farm, and it works in a populated server. Having blocks in an area above level y128 can decrease efficiency of mob spawning, since it has to account for more chunks, though, so here are some other options:

If you want to make a less tall, but still efficient design you can locate the player above the farm so that the despawn radius includes the spawner but excludes the rest of the world. Note that this design is better suited for AFKing, since you will have to make many trips up and down for this to work. This can be used for witch farms, as well as hostile mob farms.

You can also "sanitize" a 128 radius area, by lighting up every cave and surface you can find. This is obviously quite tedious, but it can allow for a ground-level farm that is active no matter where the player is. This works for witch farms as well, and is probably your best efficiency if you are playing on a server.

You are standing 32 blocks away. Mobs spawn when you are at least 24 blocks away, but then despawn over time when they are 32 blocks or more away. The other thing is, you're standing at Y = 78. I'm willing to bet that you're within 128 blocks (spherical) of some caves somewhere, which are likely filling up with mobs (there are thousands of spawning spots in caves vs. likely a few hundred in your mob spawner), and they are keeping mobs from spawning in your trap. Between this and the fact that you are 32 blocks away means it is likely that the few mobs that are spawning could despawn before you have a chance to kill them. Finally, mobs freeze (don't move) when you are around 30 blocks away, so unless your pads are small, the mobs will stop walking before they walk off the edge into your water streams, assuming you're using that style of mob trap. This means they will stand up there till they despawn.

Recommendations: use small (3x3) spawning pads, with water streams in 2-block-deep trenches between them, and make it small enough that the mobs are quickly funneled into your trap before they have a chance to despawn. Etho has a very simple mob trap design that is easy to build, expandable, and efficient, and has remained so since he designed it over 2 years ago. I would stand somewhere at least 24 blocks away horizontally, around midway up the spawner and at least 128 blocks away from any caves that aren't lit up. Since mobs do walk around for a few seconds before freezing, with this mob farm, the mobs are funneled into your trap before they have much chance to despawn, so being over 32 blocks from some pads isn't a problem.