Did vertebrates diverge from other deuterostomes via neoteny?
echinoderms are sort of bilaterally symmetrical, imagine if you took a velvet worm and then twisted it around in a big loop with the legs sticking out until the head was stuck to the tail end but still pointed away from each other. That is basically how echinoderms went from bilateral to radial. of course in practice this is done by rearranging hox genes but it is a good way to visualize it.  https://evodevojournal.biomedcentral.com/articles/10.1186/2041-9139-5-22

as for chordates look at hemichordates (which also have endoskeletons) and you can see why the general belief is that tunicates evolved that life stage after branching off(kinda like barnacles) instead of vertebrates losing that life stage.