So the Federation designs ships that aren't "sentient" but regularly created holographic entities that are. While 60s Trek would go in knee-deep with metaphor and philosophy, 90s-Trek onward, as it went along, stopped doing that as much - VOY was good at times but it was definitely playing cookie cutter with previously successful motifs, as if trying to be TNG-Lite because DS9 was too gritty or too serialized or what not. I can imagine it right now: "Oi, remember how Data was deemed being and not a tool? Let's do that with a hologram as it'll be new and cool! They did that with Moriarty, but that was by accident. Ours will be deliberate! Oh wait, they had a story later where ship became sentient? Oh wait, that's in season seven and nobody remembers that little escapade, or those that do rated it 2 stars so we're good! Make him just like the original Dr McCoy with that catchphrase, too!" So now imagine the EMH trying to leave Starfleet with another rehash of "Measure of a Man", at least prior to the appropriation of the mobile emitter technology.
There seems to be a distinction between a hologram and an android.
Both are AI and essentially synthetic in origin, but an adroid technically has a synth body... the Doctor is still a hologram though.
In fairness, if that's the case, then its an obvious distinction in how synthetic life is viewed.
Perhaps holograms are seen as less of a problem vs androids?
Also, I don't think the UFP frequently goes around making sentien holos - in most situations 'true intelligence holos' were made accidentally.
EMH's had a degree of sentience to them, but they were more akin to LLM's like ChatGPT is today (or at least, that's how they started out - a tool).
They understand who and what they are and what their purpose is and had no issues with it (much like Zimmerman diagnostic tool). Besides, the majority of EMH Mark 1's never went beyond their original programming like the Doctor had (and even in his case, it was dicey at best).
Remember when the Doctor was suffering from a cascade failure and they had to graft a diagnostic version of Zimmerman onto his matrix to stabilize him?
That and Torres did install some preventative buffers prior to that to ensure he wouldn't degrade (which were said that they didn't help - but its possible they contributed somewhat to help the EMH get through that ordeal).
I would say 'The Swarm' was a turning point for the Doctor... and its likely that what Torres did, and also subsequently grafting Zimmerman's matrix onto the EMH's is what helped turn things around for the EMH to get him to a place where he would achieve real sentience.
What grates me about ST:Picard is that it essentially showcased exactly what they feared would come to pass in 'Measure of a Man'.
That said, they didn't even NEED androids to do any kind of work next to pre-existing drones, replicators, transporters, tractor beams, and anti grav units.
I mean, come on, just make an assembly line of sorts integrating these technologies into one and you don't even need pairs of hands walking on feet to do anything (at least not as far as Trek tech is concerned).
VOY did take Treknobabble, which was an art form in TNG, and cookie cuttered it as well. Even the cream of the best episodes had at least one line of dialogue that reeked this. Even "Timeless" with its 'Borg temporal transmitter", but it's a small compromise for an otherwise very satisfying ending. Considering that was the 8 zillionth new way to do time travel, I'm surprised that the Federation didn't provide EZ instructions into every computer on how to warp around the sun or get some kemacite or replicate the Borg temporal transmitter (for which a Borg could just travel back and time and save millions of drones from being murdered because their goal has always been to elevate and improve the quality of life (from their POV) of all lifeforms, that's 100% in their charter and such...)
To be fair, that could be considered a breach of Temporal Prime Directive.
But the solution is obvious - keep it behind a firewall and let the computer only allow it if a justifiable enough reason is provided to use this method of time travel.