This has been known about since R7 launch when it first appeared, but we haven't heard official word back from the devs acknowledging the behaviour, or confirming that it's even regarded as a bug. Figured I'd post it here to get some closure on the issue.
Shotguns (including the HEL shotgun main and the pump, choke, and combat shotgun specials) appear to shoot in the direction that the model is pointing, rather than towards the centre of the player's target reticle. This is most problematic as the player swaps to shotgun, as it can lead to a shot fired during the swap animation landing below and to the left of the reticle. To my knowledge all non-shotgun guns shoot at the centre of the player's target reticle at all times, including during the swap animation.
The problem can be mitigated partially by using aim-down-sights while swapping, but even then there is an observable effect, as can be seen in RyK's footage:
#gtfo-media message
The GTFO modding community has a fix for the bug, which is available here:
https://gtfo.thunderstore.io/package/Untilted/ShotgunCenterFire/1.0.1/