re: What purposes does the vaccine serve for people that have beaten covid?

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than getting a shot of the watered down virus

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This is not even a close approximation of any of the 3 US vaccines.

The main issue between the vaccines and natural infection is the vaccines will elicit a less variable immune response across individuals due to the even dosing. The immune response to a natural infection can vary quite significantly. One could have a very mild case where only the innate immune response is activated and enough to fight off the virus and others will activate the adaptive immune systems so you get a specific immune response. This will vary from individual to individual. AFAIK there have not been any significant studies in this area and while tests are available which give a better picture than just an antibody test they are not widely used post COVID infection.