Seems like none of that should be a problem for a spy organization with unlimited resources whole sole purpose is to eliminate synthetic life.
This stuck out to me as well when the the secret of the Zhat Vash was introduced. Their secret is...that they hate androids.
This secret that could destroy a mind slips out once one Romulan gets drunk. Sounds like this secret would be very hard to keep all these years.
And it's not presented like it's this fringe group of radicals that just seized power and resources in the last 10-15 years, or that they were suppressed, or that it was just a matter of funding. The impression is that yes, there's the there's the secretive Tal Shiar organization, but there's an even
more secretive organization, the Zhat Vash. So the impression is that they were two organizations operating simultaneously but that one was even more covert and secretive than the other because of the "secret."
Had the Zhat Vash been introduced as this obscure cabal of cultists who seized power in between TNG and PIC it might make a little more sense. But the way it's introduced it comes across like a very blatant retcon.
It seems like Data would have been a prime target for assassination or deconstruction. Romulans were depicted as very clever, like when they fed their own generals disinformation in order to test their loyalty, all in order to lure a Federation starship into a trap so they could capture the crew and ship itself. Something similar could have been done to get at Data.
But they didn't have the resources.
That still doesn't satisfy the retcon. If the Zhat Vash truly believe that a synthetic being could bring about the mass destruction of worlds, the destructor, they would FIND a way to get at Data. Some kind of attempt.
We might get a more explanation on the history and structure of the Zhat Vash but the way it was introduced seemed out of left field. It's just one of those things you gotta overlook in order to enjoy the ride. The other expansion on Romulan culture is enough to distract from any possible plot holes with the Zhat Vash.