In the attached world, if you open the chest (without moving around or turning the camera), it sounds like it's coming from your right, despite the chest being almost directly in front of you. Move the camera slightly and it sounds normal again.
This seems to be related to distance. Walking around and destroying the trees and grass around you in the attached world (almost 30 million blocks out), you can hear similar things happening.
Reproduction steps which do not require a world download are forthcoming.
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Please read the moderator note on MC-121364

@unknown: This is a distinct problem. It’s a floating-point precision issue. Note that the chest is mostly centered in view, nowhere near the 30 degrees indicated there for a hard pan. Note that the save puts you out at 30 million blocks. This problem does not occur near the origin. 32-bit floats have a precision of 2 blocks at 30 million, which seems about right given the way it sounds and changes in distinct steps as you move around. With all the recent changes in this regard like particles getting proper precision, it’s only natural for audio to follow suit.

Can reproduce in 20w30a using a setup with a double chest at 20 million blocks out - minor movements to the left and right cause greatly exaggerated differences in sound origin position, which does not happen close to spawn. The chest must be setup in the right position though, such that the origins of the sounds are separate.
[media]

Can confirm for 1.16.2 pre1

Can confirm for 1.16.2pre2

Affects pre3

Affects 20w45a

Affects 20w46a

Affects 21w03a

@Mods feel free to reassign this to Connor

Can confirm in 1.17 Pre-release 2

Can confirm 1.17 Pre-release 3

Probably relates to MC-177725.

Can confirm in 21w41a.

can confirm for 23w07a
This has gotten worse in more recent versions (somewhere after 1.16)

Has gotten MUCH worse in 1.20 and 1.20.1, now the corrupted and off-positioned sound is very apparent even within vanilla bounds especially past 16777216.

can confirm this for 24w14a

Can confirm for 1.21.3.

Mojang, please add a gamerule to remove the world border. Literally nothing is stopping you from doing that, as you can see in this reference video.

Can confirm in 1.21.4 prerelease 1.

Can confirm in 1.21.4 release candidate 3.

Confirmed in 1.21.4