The closest, I think, this relates to in official content is "Symbiotic Entity"
TL;DR: YES (but it may be subject to order in which it is done, Wild Shape 1st, Starry Form 2nd)
From Guildmaster's Guide to Ravnica (GGR) page 27, for the Circle of Spores druid
It says in part:
Symbiotic Entity: [..] As an action, you can expend a use of your Wild Shape feature to awaken those spores rather than transforming into a beast [..]
If it is similar, as in Symbiotic Entity is "akin/equal to" Starry Form, which I am "assuming", then I believe that your Starry form "is your wild shape" or at least, counts as a use of the "wild shape" (Out of your total available uses of wild shape).
Starry Form: [..] As an action, you can expend a use of your Wild Shape feature to take on a starry form rather than transforming into a
I'm re-reading the "Symbiotic Entity" entry, if they are "similar" this (your "Starry Beast Form") would be possible ...its 2 uses of wild shaping, the 1st on a "beast form", then the 2nd into special "Starry Form". RAW this is ok, from my understanding.
HP hitting "ZERO" (0) in this STARRY BEAST FORM but not being incapacitated when you revert to STARRY NATURAL FORM, as per PHB pg 67:
Wild Shape: [..] if you revert as a result of dropping to O hit points, any excess damage carries over to your normal form [..]
You would revert you to your "natural state" (un-does WildShape), but you would continue to be in your "Starry Form" until it otherwise is ended, form from the UA "Circle of the Stars" text:
Starry Form: [..] The form lasts for 10 minutes or until you’re incapacitated. [..]
So turning into a beast would add to "Starry Form" as long as "Starry Form" was done 2nd. IF MY ASSUMPTION IS CORRECT, the wording is clearer for the spore druid mind you (UA can be iffy).
See HERE, for related (and maybe needed) "Can a druid wildshape again whilst still in animal form?"
Can everyone say "Starry Deinonychus"... yep, knew you could
I'm calling this a UA misstep, "error of omission" or commonly ..."a big typo".
UA can be fun, but it can be "half-baked", needing another dev team pass after all the "play testers" have weighed in with opinions. Until its "officially" given the official seal, like the Artificers was, it may be "iffy" to use RAW without "table rulings"
But using the Text in Circle of Stars (UA) & comparing it to "similar text" in official content of Circle of Spores (GGR). I would read this as 100% possible, neither "special form" says anything about requiring you NOT to be in Wild Shape to access these features, so they may be used complimentary to each other. Starry Form benefits much more from Wild Shape than Symbiotic Entity (as the only "Beasts" able to use melee weapons are Ape/Giant Ape MENTIONED HERE, so 99% are "not using" half that features benefit..& Giant Ape is an Level 20 "Epic Boon"), but both are possible