Yeah, they'll eat Aquilonastra ("Asterina") stars, sponges, tunicates, etc. They're thought to be biofilm eaters in the wild, but - as you've noted - they'll occasionally scavenge for food too:
Yeah, some people believe that the "Asterinas" (technically Aquilonastras) the Linckias eat allow their stars to survive in their tanks - I've suggested people may want to try farming them to feed their Linckias as a result. They likely do also eat tunicates and sponges, as those tend to be bacterial sinks (so they'd basically replicate biofilm for the stars to feed on).
Genuinely glad to hear they're doing well for you - please keep us updated on how it goes, as most of the time I've heard these stars typically die off around ~8-13 months in our tanks (though I've heard of them making it to ~2-3 years if there are Aquilonastra stars in the tanks with them - they seem to basically wipe the Aquilonastra population out after/around that time).
One important thing to keep in mind with foods for these guys - just because they eat it, doesn't mean it's meeting their nutritional needs; it might be, but it might not be. With how long it seems to take these guys to starve, unless you're monitoring their health closely, you might not notice if it's not meeting their needs until it's too late.
Some ways to potentially gauge the health of the starfish that may be useful:
1 - Visual: is anything visually wrong with the specimen? (From what I know of starfish, these cues are generally pretty obvious if they're there at all - if the starfish is disintegrating, there's something wrong). [Edit: you may also be able to tell if the star is looking lean/gaunt or full/puffy; gaunt is generally not good.]
2 - Weight: is the specimen putting on or maintaining weight (generally healthy), or is it losing weight (under most circumstances, this would be unhealthy)?
3 - Size/Length: if it's not already full size, is the specimen growing? Is it shrinking (either from weight loss, disease, limb loss, etc.)?
4 - Reproduction: is the specimen engaging in reproductive behaviors/activities (i.e. courting, nesting, spawning, etc.)? (I recognize this one is not as common of an indicator in captive starfish at this point, but there are a few instances of starfish attempting to spawn in captivity).
5 - Longevity: is the specimen relatively close to meeting, actually meeting, or exceeding their expected wild lifespan (or at least surviving for a few years - healthy), or is the specimen dead/dying prior to doing so (unhealthy)?
6 - Speed: how quickly can the specimen right itself when it's flipped over?
7 - Level of activity: how much is the specimen moving around? (Generally speaking, low activity indicates poor health; moderate activity indicates good health; and high activity indicates good health but probable stress - it could be searching for food, oxygen, etc., but it's probably not in terrible health when moving a lot).
8 - Grip strength: does the specimen have a strong hold/grip with its tube feet? (A strong grip indicates good health, a weak grip indicates poor health).
9 - Willingness to eat: is the specimen eating? (Seems obvious, but can be really hard to tell with some stars - some stars leave little trails called feeding scars through the things they're eating; sometimes you can see their everted stomachs; other times, like if they're feeding on biofilm, you may not be able to tell at all - them crawling onto visible food is a good sign they're willing to eat, but - as mentioned above - the food may or may not meet their nutritional needs).
