The bug

When a sound is played using /playsound, it can be heard in all dimensions (assuming the player is near the coordinates from which the sound is played), no matter which dimension the command was executed in.

For example, let's take this command:

/execute at @s in minecraft:the_end run playsound block.anvil.land master @a ~ ~ ~ 1 1

Since the command is executed in the end, what should happen is the sound can only be heard when in the end, but not when in another dimension. What actually happens is the player hears the sound no matter which dimension they're currently in (including custom dimensions from a datapack).

This isn't due to using @a since the selector here is only used to select which player is eligible to hear the sound, and if the player is too far away the sound will not be played (and it shouldn't be played if the player is in another dimension as well).
Also, with /particle, even if @a is specified, the player will not see particles regardless of dimension, but only in the dimension the command was executed in (distance also can prevent the particles from being displayed if the mode isn't set to force).