Sounds work cross-dimensionally with /playsound.

Explanation:

If the command: "/execute in minecraft:the_end run playsound <sound> master @a" is run in the overworld, the selected sound will be heard at the position the command is run from. This does not make sense as the sound is being played from the end dimension and as sound mechanics are based around distance there should be no way for the sound to reach the player.

Theory:

I would guess that the problem is in the /playsound command and how sounds work in general. When a sound is played for a player it is filtered based on coordinate differences (so you can't hear something 1000 block away) but only these. With most sounds, this would work fine cross-dimensionally as they would filter players to be played the sound based on their dimension. /playsound's filter doesn't have this fail-safe as it is defined by the player and only filters sounds based on coordinate distance.

Versions:

I haven't tested this bug on any version other than 1.16.3 (so I wouldn't trust my evaluation) but I would guess it is a bug in any version of the game with /playsound and target selectors able to be used cross-dimensionally (they may always have been able to be used as such).

Note:

The command example I gave works with other dimensions. I chose to use the end because it has no dimension scaling relative to the overworld. Using the nether you would want to go near to 0,0 to hear the sounds.