Capture Eggs!

The Capture Eggs can be crafted with 4 Blaze Powder in the corners of the crafting table, 4 eggs on the edges and 1 Shulker Shell in the middle, as shown in the images. You get 4 Capture Eggs from this recipe.

A Capture Egg also has a 1 in 1000 chance of dropping from a chicken on death, and a 100% chance of dropping from a chicken killed by the player while the chicken has the Wither effect.

A trapped mob spawn egg will be of the same type as the captured mob. If the mob is named when it is captured, the egg will be named as well.
The lore of the spawn egg contains details about the mob, including mob type, health, villager profession(if applicable), slime and magma cube size(if applicable), whether the mob is a baby and whether the mob is on fire.
If you capture a mob naturally immune to fire, the egg will also be immune to fire, signified by the lore text Fire Resistant.

Finding which mob was hit by the capture egg is relatively tricky, so sometimes it can make mistakes. With a recent fix it is now very reliable, but it can still have trouble if you want to trap a specific mob within a big group of mobs. To make it more reliable, you can throw the egg from an angle where it doesn't pass any other mobs, and make sure none of the other mobs are taking damage.

Whenever you capture a mob a firework blasts. I've tried my best to make sure this can't hurt anything, but it still gives a damage tick (with no damage) to nearby entities.

Capture Eggs must be thrown by a player to capture a mob, otherwise they will act like normal eggs.

Capture Eggs can still spawn chickens, I couldn't figure out how to remove this.

Download the ZIP file, and either drag into the datapacks folder of an existing world, or add to a new world during creation.
I have designed it so that no extraction of files is required.