It’s complicated! No surprises there 
However, I will try to explain in a few bullet points, while bearing in mind that famous utterance by Donald Rumsfeld ‘there are known knowns; there are things we know we know. We also know there are known unknowns; that is to say we know there are some things we do not know. But there are also unknown unknowns—the ones we don't know we don't know’
As you pointed out, viruses evolve. They usually mutate in response to the spread of the infection. Viruses want to survive, and as they can’t reproduce on their own they need a host (in this case humans) to grow and multiply. As humans develop immunity, viruses need to change so they won’t be susceptible to the existing human defence system (the immune response). Antibodies are not the only arrow in the immune response arsenal, special virus-killing cells called T-cells are also produced.
The South African (SA) authorities have been commendably upfront about their trials of the AstraZeneca (AZ) vaccine against Covid-19 and have published detailed data on the results. The trial began before the emergence of the SA variant.
The trial used a relatively small number (under 2000) young, healthy volunteers, and the endpoint was to determine the effect of the vaccine against mild to moderate Covid-19. In order to determine the effect against severe Covid-19 a much larger survey base would have been needed.
The initial responses were very promising (up to 75% effective). However, when the virus mutated and the SA variant became dominant the efficacy of AZ decreased, and by the end of the trial 42% of the volunteers were infected with the SA variant of Covid-19.
Like the J&J vaccine, it’s expected that the AZ vaccine will be more effective against severe Covid-19.
In another trial in SA using the Novavax vaccine, this was found to be 95% effective against the original strain (which I believe is the variant we have so far controlled here in Oz), and 60% effective against the SA variant. Another caveat is that this trial included people living with HIV, so a better cohort than the above trial.
It’s important to note that although the antibody production against the SA variant of the coronavirus was poor, it seems that production of T-cells (virus killer cells) by the immune system remained good. The T-cells start killing viruses when the antibody response to the invasion of a pathogen signals them to spring into action. Vaccines exploit the body’s response by getting the adaptive immune response to start producing antibodies EARLY before a full-blown infection begins.
We MUST reduce transmission of SARS-Covid-2 (coronavirus) so that the opportunities for the virus to spread and mutate are reduced, thus increasing the efficacy of existing and future vaccines. So far there are no clear results from ANY of the existing vaccines on their efficacy against infection and transmission (spread) of the virus. This is the Holy Grail!
Cheers, h
(20min delay)