"Updated Aug. 6, 2021"

You can post something from last century, it will be as wrong as this link. Omicron has shown extremely increased reinfection risk compared to all the other variants. So the correct answer is:

yes, you absolutely do need to get a vaccine after the infection if you want to lower your reinfection chances.

They can't be that rare. I heard about multiple from my social circle.

Curious enough, almost everyone I know who had COVID once at least thinks they got it at least one more time. Obviously anecdata etc., I’m not substantiating any argument at all with this, but this fact of my personal experience didn’t occur to me until reading your comment!

Nice. We have reached the point where hearing from your social circle is equivalent to data.

It's not. However if somebody claims that something almost never happens and you, being completely average person, know few people that claim it has happned to them then something might be up.

Somebody's might be mistaken. Probably those few people but I'd like to see stronger evidence for the general claim as well.

Especially if claim is extraordinary. We know very few illnesses where being sick once gives you immunity for life.