Does that mean that bilateral symmetry evolved just once in the entire history of life? Is it correct to say then that bilateral symmetry is not a feature of convergent evolution? That this is indeed a thing that evolution explored just that time in history and never again?
A lack of strong evidence causes the field to be mostly hypothetical. Detailed pre-cambrian fossils are necessary, from the 1bn-600 million years ago, to find a protostome - deuterostome ancestor.
Genetic data is also inconclusive. A search for bilateral common ancestor gives i.e. dev.biologists.org/content/129/13/3021 It's a summary of research, where the accepted view is that there is a common ancestor to all known bilateral organisms.
All the baliteria are classed in the common clade which have a similar cell attributes and physiology, they all have hearts whereas starfish and jellyfish don't, there are various genes that suggest common ancestry. There is currently no evidence of bilateral from parallel evolution, although it's very possible or probable that there were some previously and perhaps even today, i.e. tardigrades don't have hearts, so perhaps some species one day will be found to be convergeant species, although they are thought to be miniaturized lobopodia.
Sea cucumbers and sea anenomes both have a bilateral juvenile stage, so they have perhaps evolved from bilateral ancestors. researchgate.net/profile/Taha_Soliman4/publication/262415405/…
A new fossil of a bilateral animal has been found from 550mn years ago: phys.org/news/2020-03-ancestor-animals-australian-fossils.html squids are starfish with mollusks on them, there are hybrid symmetries.