If you are vaccinated and asymptomatic, you're probably not likely to be contagious, even if you technically do have some Covid virus from an exposure.
This was discussed as a possible concern back when the vaccines were first rolled out, but the authorities (CDC/WHO/etc) soon claimed good evidence that vaccination was preventing transmission.
The "defense in depth" advice is still good (don't go mixing with people if you don't have to), but I don't think this is a big worry.
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