You are correct.
The strains are identified by genomic sequencing, not PCR.
Not full sequencing— the “variant” is the S-Protein genomic, and unless they can match every single instance of the FULL genomic for a “new” variant— that is for the entire S-Protein encoding, it cannot be proven to do anything this “article” says it is able to do.
The natural immunity of survivors of Covid-19 is not only to the infection modality, but also to the full virion genetic component, that is, the complete code of the infection virus inserted by the mRNA in those who were infected by the virus from the virion.
They will have to have a lot more data to make broad statements about immunity.
Spanish influenza as a mutation remains in the world, and has mutated many times since. And the sequence is included in every year’s influenza formula.