Well, normally I’d say the common name of Biscuit Sea Star is used for a number of different species, and knowing which one you’re asking about specifically would be helpful, but there’s actually some pretty good info available for most of the different species it could be in this case, and they seem to all have similar needs - so I’ll skip that common name bit this time.
It looks like they prefer areas with lots of rock and rubble (intertidal zones, rocky reefs, rocky shores, etc.), and they seem* to feed on algae, sponges and other filter feeders (like tunicates), bryozoans, and “encrusting animals” - whatever that actually means.
*with starfish, seeming to eat something does not necessarily mean they’re actually eating it or getting nutrients from it, just to clarify.
Having done some extensive study on different starfish (and a limited number of sponges), this starfish actually seems to be a relatively good aquarium candidate at the moment when compared to other starfish. However, that doesn’t make it an actually good candidate overall when looking at keeping it long term (i.e. for ~2+ years) - at least not yet. You’d need to figure out a solid diet for it first. This is a problem for a number of reasons.
For one thing, figuring out which sponges it’ll actually eat may be tricky, as a number of different sponges produce chemicals specifically to try and drive predators (like this starfish) away, and you’d want to grow the sponges it will eat yourself so you can be sure you’re able to keep it fed. Beyond that, it might need more variety than just a sponge species or two to keep it healthy, so you’d probably want to figure out what tunicates and other things it’ll eat too - and you likely need to grow those out yourself as well. Plus, as mentioned above, keeping nutrients in hand while keeping all of these things alive could prove quite challenging (though this is easier with larger tanks).
Assuming you’re up for trying though, I’d recommend starting with a handful of different sponges - photosynthetic plating sponges, ball sponges, tree sponges, Haliclona sponges, crumb of bread sponges, chicken liver sponges, etc. are a few you could try - and seeing how you do with them first, then add the starfish. If it eats any of those, make a note of it and see what else it eats. If not, find something else to offer it and try that until you get it eating. Once you’ve got something you feel confident it is eating growing, you can keep offering it new things to try and expand its diet (and I’d recommend doing so), but, most importantly, you’d want to see how it does long term. Track how long it lives on the diet you’re feeding it, and if it makes it to two years or more, let us all know.
