(The theory is that the vaccine antibodies do a better job of binding to the active site on infectious virus particles than the antibodies induced from infection, which bind to whichever part of the virus, and may bind to the form the active site takes after attaching to a cell, rather than prior)

Also, getting the vaccine as early as it is available is a better way to avoid long Covid than getting the vaccine after you've had a course of infection.

I don't think so. We have multiple links in this thread that say otherwise.