I mean... yeah, the episode isn't as focused on procedural detail, and I do live for legal process minutia, but I can fill in the blanks just fine and suspend disbelief.
I mean, the question being raised is whether Data has been operating as a person willingly joined Starfleet or as salvaged equipment. If Data had been roaming around on his own and then applied to join Starfleet I'd be more nitpicky, but he was found and turned on by Starfleet and he seems to have been in the system since, so I can see the question of how to categorize him coming up retroactively. Especially in retrospect, since we eventually get undeniable confirmation that AGI is very much possible within their normal gear.
I mean, for the record, by the time Voyager comes around we know that they have protocols to use holographic AIs to substitute in for key personnel, so if you can have a "EMH" slot in for an officer you can have a piece of salvaged machinery operate with a rank and then reassign it to a different role... unless that entity has personhood. It IS a sci-fi as hell concept, but a valid one in-universe.
Me, I would have very much enjoyed Noonyien Soong arguing whether he still owns Data and learn what is legal salvage in Starfleet territory but for the sake of 90s network TV I can see "Is this android truly a life form" being the approach to a Trek episode. And thematically... well, I can't get through the Goldberg and Stewart scene about slavery without tearing up. It isn't just how good they both are, it's the "oh, crap, they're saying the thing" element to it, too.
Of course that means Starfleet straight up condoned slavery later, as per Star Trek Picard season 1. I would gladly remove all of Picard from lore at this point, but nope, officially Starfleet had legal proceedings to determine that Soong androids are people and to remove their autonomy is akin to slavery and then went ahead and did it anyway.
Picard sucks and is the worst Star Trek thing ever, is what I'm trying to say. Yes, way worse than anything in Discovery. Including season three.