The way the immune system works is that specific immunity to anything (whether virus or bacteria; first infection or recurrence) will only kick in after the infection gets into you, & the innate (non specific) immune response cells presents the pathogen to your T and B cells
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So any vaccine, will only help you clear the pathogen quickly before it causes harm or disease. No vaccine can actually prevent the pathogen from entering the body in the first place. It can only help you clear the virus or bacteria quickly.

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So during the time span from when a virus enters the body and when it is cleared by the specific immune response, a person is at least theoretically infectious. But it will be much shorter time span if someone has pre-existing immunity from prior natural infection or vaccine
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Normally this time span is not a problem coz most diseases unlike COVID are not totally new to the world and there is some level of population immunity, and many not spread so easily. So until we have more data or reach herd immunity better to wear a mask even after a vaccine
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The that we are asking people to be cautious and wear a mask after infection or vaccine doesn’t mean that vaccines don’t work or that natural infection doesn’t provide immunity. It’s only to reduce risk

It’s also not permanent. I’m guessing 4-6 months for many parts of the world