I had the COVID in Feb 2020. I got fully vaxxed in May 2021.
Has there been a study of how much protection there is for a person who got both the natural immunity to the virus AND the vaccine?
What you did is very smart! you should have excellent protection going forward.
A few points to keep in mind. The level of infection affects the scale of host's immune response. A positive covid test alone is not proof of infection, particularly if a high number of rt-PCR cycles is needed to give a positive response. PCR responds to non-viable virus the same as to viable. PCR can yield a positive response even if the viable viral count is so low that their is a low probability of the virus successfully invading its host and reproducing... The most reliable diagnosis, beyond doing viral cultures which replicate only viable virus and are usually carried out only in research studies, is achieved via a combination of a positive PCR test and the presence of characteristic symptoms. A fever alone, for example, is not sufficient. Symptomatic diagnosis alone is better than PCR alone, but PCR combined with several symptoms is more reliable. It is now thought that the reason there were so many asymptomatic infections being reported from PCR testing is some of these subjects were not infected despite testing positive. PCR can in theory detect a single virus, viable or non-viable, but of course such low levels of contamination are highly subject to sampling error. PCR screening, however, is excellent for determining who should be quarantined and watched closely for development of symptoms.
In the initial phases of the U.S. Covid Pandemic, the U.S. was unprepared for massive PCR testing and did not do nearly enough testing. Testing was essentially limited to those with symptoms, whereas what was needed was massive testing of the asymptomatic, in an attempt to head off a pandemic.. What testing was being done was mostly with highly unreliable, at least at the time, dipstick type antibody tests, similar to the test your physician uses to check for the flu . Now these tests are more reliable for covid. Because of inexcusably poor national coordination of testing and reporting protocols, early testing was reported piecemeal by States and antibody and PCR results were often combined without distinguishing them. This is why the Biden CDC found the earlier data not very useful.
Recall "virologist" Pence was put in charge , and the States were left on their own to figure out what to do, meanwhile the administration continued to interfere with CDC policy and edit CDC communications to the public. On the theory that perception is more important than reality, the administration's efforts were aimed at reporting as few infections as possible, as opposed to having as few infections as possible. Things did not begin to get straightened out until the Biden administration took the helm. There was a policy of non-cooperation in the Trump administration which did not even recognize the incoming administration until the last days when it had no choice.